The Experts below are selected from a list of 203400 Experts worldwide ranked by ideXlab platform
Lutful Bari Bhuiyan - One of the best experts on this subject based on the ideXlab platform.
-
Structure functions of rod-like DNA fragment and polystyrenesulfonate solutions in the modified Poisson-Boltzmann theory
Physica A-statistical Mechanics and Its Applications, 1996Co-Authors: Lutful Bari Bhuiyan, Christopher W. Outhwaite, J. Van Der MaarelAbstract:The partial structure functions of aqueous solutions of rod-like DNA fragments and polystyrenesulfonic acid are calculated in the modified Poisson-Boltzmann theory. The cylindrical cell model appropriate for linear polyelectrolyte solutions with monovalent counterions and without any added salt is utilized. The predicted results are compared with the corresponding results from the classical Poisson-Boltzmann theory, and experimental small angle neutron scattering data obtained in the monomer concentration range 0.05-0.2 mol/dm3. It is seen that both the modified Poisson-Boltzmann and the Poisson-Boltzmann results lead to a very good fit to the experimental structure functions.
-
Micellar solutions with added salt: A Monte Carlo and modified Poisson-Boltzmann study
Molecular Physics, 1995Co-Authors: M. Lanza Amaro, Lutful Bari Bhuiyan, Christopher W. OuthwaiteAbstract:The spherical cell model is used to investigate the structural and thermodynamic properties of common micellar solutions with added salt. The model is analysed using Monte Carlo simulations, the classical Poisson-Boltzmann theory, and the modified Poisson-Boltzmann theory. It is seen that for monovalent systems the modified Poisson-Boltzmann theory can reproduce the Monte Carlo results accurately over a wide range of polyion and added salt concentrations. The structural predictions of the Poisson-Boltzmann theory on the other hand, deviate from the Monte Carlo values at higher concentrations although the predicted osmotic pressures are surprisingly good. For divalent systems the Poisson-Boltzmann theory is useful at low polyion and salt concentrations with the modified Poisson-Boltzmann thermodynamic results being generally closer to the simulations.
-
Structure and thermodynamics of micellar solutions in the modified Poisson—Boltzmann theory
Chemical Physics Letters, 1992Co-Authors: Lutful Bari Bhuiyan, Christopher W. Outhwaite, Dusan BratkoAbstract:Abstract The modified Poisson—Boltzmann theory, in conjunction with the spherical cell model of colloidal dispersions, is applied to a study of structural and thermodynamic properties of micellar solutions. The concentration profile of the small, simple ions with respect to the polyion, and the osmotic pressure are evaluated for different values of polyion surface charge, polyion radius, and cell radius. Comparisons are made with results from the classical Poisson—Boltzmann theory and Monte Carlo simulations. The osmotic pressures are also compared with those available from the anisotropic hypernetted chain theory. It is found that the modified Poisson—Boltzmann equation accurately represents the simulation results for monovalent simple ions, with the Poisson—Boltzmann equation only being adequate at low ionic concentrations. For divalent simple ions the thermodynamic properties of the modified Poisson—Boltzmann are superior to the other theories whereas its structural properties show improvement upon the Poisson—Boltzmann predictions only at large distances from the polyion.
Dusan Bratko - One of the best experts on this subject based on the ideXlab platform.
-
Structure and thermodynamics of micellar solutions in the modified Poisson—Boltzmann theory
Chemical Physics Letters, 1992Co-Authors: Lutful Bari Bhuiyan, Christopher W. Outhwaite, Dusan BratkoAbstract:Abstract The modified Poisson—Boltzmann theory, in conjunction with the spherical cell model of colloidal dispersions, is applied to a study of structural and thermodynamic properties of micellar solutions. The concentration profile of the small, simple ions with respect to the polyion, and the osmotic pressure are evaluated for different values of polyion surface charge, polyion radius, and cell radius. Comparisons are made with results from the classical Poisson—Boltzmann theory and Monte Carlo simulations. The osmotic pressures are also compared with those available from the anisotropic hypernetted chain theory. It is found that the modified Poisson—Boltzmann equation accurately represents the simulation results for monovalent simple ions, with the Poisson—Boltzmann equation only being adequate at low ionic concentrations. For divalent simple ions the thermodynamic properties of the modified Poisson—Boltzmann are superior to the other theories whereas its structural properties show improvement upon the Poisson—Boltzmann predictions only at large distances from the polyion.
Christopher W. Outhwaite - One of the best experts on this subject based on the ideXlab platform.
-
Structure functions of rod-like DNA fragment and polystyrenesulfonate solutions in the modified Poisson-Boltzmann theory
Physica A-statistical Mechanics and Its Applications, 1996Co-Authors: Lutful Bari Bhuiyan, Christopher W. Outhwaite, J. Van Der MaarelAbstract:The partial structure functions of aqueous solutions of rod-like DNA fragments and polystyrenesulfonic acid are calculated in the modified Poisson-Boltzmann theory. The cylindrical cell model appropriate for linear polyelectrolyte solutions with monovalent counterions and without any added salt is utilized. The predicted results are compared with the corresponding results from the classical Poisson-Boltzmann theory, and experimental small angle neutron scattering data obtained in the monomer concentration range 0.05-0.2 mol/dm3. It is seen that both the modified Poisson-Boltzmann and the Poisson-Boltzmann results lead to a very good fit to the experimental structure functions.
-
Micellar solutions with added salt: A Monte Carlo and modified Poisson-Boltzmann study
Molecular Physics, 1995Co-Authors: M. Lanza Amaro, Lutful Bari Bhuiyan, Christopher W. OuthwaiteAbstract:The spherical cell model is used to investigate the structural and thermodynamic properties of common micellar solutions with added salt. The model is analysed using Monte Carlo simulations, the classical Poisson-Boltzmann theory, and the modified Poisson-Boltzmann theory. It is seen that for monovalent systems the modified Poisson-Boltzmann theory can reproduce the Monte Carlo results accurately over a wide range of polyion and added salt concentrations. The structural predictions of the Poisson-Boltzmann theory on the other hand, deviate from the Monte Carlo values at higher concentrations although the predicted osmotic pressures are surprisingly good. For divalent systems the Poisson-Boltzmann theory is useful at low polyion and salt concentrations with the modified Poisson-Boltzmann thermodynamic results being generally closer to the simulations.
-
Structure and thermodynamics of micellar solutions in the modified Poisson—Boltzmann theory
Chemical Physics Letters, 1992Co-Authors: Lutful Bari Bhuiyan, Christopher W. Outhwaite, Dusan BratkoAbstract:Abstract The modified Poisson—Boltzmann theory, in conjunction with the spherical cell model of colloidal dispersions, is applied to a study of structural and thermodynamic properties of micellar solutions. The concentration profile of the small, simple ions with respect to the polyion, and the osmotic pressure are evaluated for different values of polyion surface charge, polyion radius, and cell radius. Comparisons are made with results from the classical Poisson—Boltzmann theory and Monte Carlo simulations. The osmotic pressures are also compared with those available from the anisotropic hypernetted chain theory. It is found that the modified Poisson—Boltzmann equation accurately represents the simulation results for monovalent simple ions, with the Poisson—Boltzmann equation only being adequate at low ionic concentrations. For divalent simple ions the thermodynamic properties of the modified Poisson—Boltzmann are superior to the other theories whereas its structural properties show improvement upon the Poisson—Boltzmann predictions only at large distances from the polyion.
Roger G. Melko - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Boltzmann Machine
Physical Review X, 2018Co-Authors: Mohammad Amin, Evgeny Andriyash, Jason Tyler Rolfe, Bohdan Kulchytskyy, Roger G. MelkoAbstract:Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative nature of quantum mechanics, the training process of the Quantum Boltzmann Machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors like D-Wave for QBM training and application.
-
Learning Thermodynamics with Boltzmann Machines
Physical Review B, 2016Co-Authors: Giacomo Torlai, Roger G. MelkoAbstract:A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.
Lishi Luo - One of the best experts on this subject based on the ideXlab platform.
-
Lattice Boltzmann model for binary mixtures.
Physical Review E, 2002Co-Authors: Lishi Luo, Sharath S. GirimajiAbstract:The lattice Boltzmann equation ~LBE !@ 1‐6 # is emerging as an effective computational method based on fundamental physics for simulating complex flows such as multiphase @7‐10# and multiple-component flows @11‐13#, flows through porous media ~cf. Ref. @5#!, and particulate suspensions in fluid flows ~e.g., Ref. @14#!. Recently, important strides have been made on the theoretical front, establishing, from fundamental principles, the physical legitimacy and mathematical rigor of the LBE method. Most importantly, it has been proved that the lattice Boltzmann equation can be derived from the Boltzmann equation a priori @2‐ 4,9,10# .I t should be pointed out that the Boltzmann equation bridges the gap between the microscopic dynamics and the macroscopic hydrodynamics. Indeed the Navier-Stokes equations can be rigorously derived from the Boltzmann equation via the Chapman-Enskog analysis. The second important theoretical result is the demonstration that the lattice Boltzmann equation is indeed equivalent to an explicit finite difference scheme of the Navier-Stokes equations @15#. These theoretical developments have completely and comprehensively resolved all doubts surrounding the early lattice-gas automata @16# and lattice Boltzmann models. The present day lattice Boltzmann equation is a viable alternative to the continuum methods for simulating fluid flows. Much of the rigorous work with lattice Boltzmann methods so far has been restricted to simple single-phase single-component fluids. Recently, the LBE model for single-component multiphase fluids has been derived from the Enskog equation @9,10# .A rigorous mathematical development of the lattice Boltzmann method for multicomponent fluids is still in its infancy and such is the object of the present work. In many practical flows involving pollutant dispersion, chemical processing, and combustor mixing and reaction, mass and momentum transport in multispecies fluids plays an important role. For these applications, the continuumbased models can be difficult to compute due to various reasons such as complexity of flow geometry and phase change. Moreover, it is difficult to construct the continuum-based models from first principles. Therefore for these flows, there is a growing interest in using the lattice Boltzmann equation @11‐13#. In this paper, we develop a unified approach for developing the lattice Boltzmann models for multicomponent fluids within the framework of kinetic theory. This work is a part of our continuing effort to set the lattice Boltzmann equation on a rigorous foundation @2,3,9,10#. Specifically, we will derive a conservative discretized version of the continuum Boltzmann equation for fluid mixtures. We shall present a model that is capable of simulating either a miscible or immiscible binary mixture. The lattice Boltzmann equation considered here can be extended to a mixture of three or more species. The kinetic theory of gas mixtures encompasses a significant amount of literature ~e.g., Refs. @17‐27#!. In a manner similar to the derivation of the Boltzmann equation for a pure system of single species, one can derive N simultaneous equations for a system of N species by reducing the appropriate Liouville equation. For the sake of simplicity without loss of generality, we shall only discuss the Boltzmann equations for a binary system, ] t f A 1jiif A 1aAiij f A 5Q AA 1Q AB , ~1!
-
unified theory of lattice Boltzmann models for nonideal gases
Physical Review Letters, 1998Co-Authors: Lishi LuoAbstract:A nonideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for nonideal gases. The existing lattice Boltzmann models for nonideal gases are analyzed and compared with the model derived here. [S0031-9007(98)06759-3]
-
theory of the lattice Boltzmann method from the Boltzmann equation to the lattice Boltzmann equation
Physical Review E, 1997Co-Authors: Lishi LuoAbstract:In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.
