Mean-field Force Research Articles

Application of Mean Field Boundary Potentials in Simulations of Lipid Vesicles

A method is presented to enhance the efficiency of simulations of lipid vesicles. The method increases computational speed by eliminating water molecules that either surround the vesicle or reside in the interior of the vesicle, without altering the properties of the water at the membrane interface. Specifically, mean field force approximation (MFFA) boundary potentials are used to replace both the internal and external excess bulk solvent. In addition to reducing the cost of simulating preformed vesicles, the molding effect of the boundary potentials also enhances the formation and equilibration of vesicles from random solutions of lipid in water. Vesicles with diameters in the range from 20 to 60 nm were obtained on a nanosecond time scale, without any noticeable effect of the boundary potentials on their structure.

QM-MM Investigation of the Reaction of Peroxynitrite with Carbon Dioxide in Water.

We have investigated the reaction of peroxynitrite with carbon dioxide in aqueous solution by means of combined quantum-classical (QM-MM) molecular dynamics simulations. In our QM-MM scheme, the reactant was modeled using density functional theory with a Gaussian basis set, and the solvent was described using the mean-field TIP4P force field. The free energy profile of this reaction has been computed using umbrella sampling and multiple steering molecular dynamics (MSMD) schemes. Umbrella sampling methods turned out to be much more efficient than MSMD schemes, due to the possibility of employing a combination of classical and QM-MM thermalization schemes. We found the presence of a significant barrier in the free energy profile associated with the reaction in solution, which is not present in vacuum, that may be ascribed to the significant charge redistribution upon reaction and the concomitant solvation pattern changes.

Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging

The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g., in microfluidic pumps and electrochemical sensors. Since the 1950s, several modifications of the PB equation have been proposed to account for the finite size of ions in equilibrium, but in this two-part series, we consider steric effects on diffuse charge dynamics (in the absence of electro-osmotic flow). In this first part, we review the literature and analyze two simple models for the charging of a thin double layer, which must form a condensed layer of close-packed ions near the surface at high voltage. A surprising prediction is that the differential capacitance typically varies nonmonotonically with the applied voltage, and thus so does the response time of an electrolytic system. In PB theory, the differential capacitance blows up exponentially with voltage, but steric effects actually cause it to decrease while remaining positive above a threshold voltage where ions become crowded near the surface. Other nonlinear effects in PB theory are also strongly suppressed by steric effects: The net salt adsorption by the double layers in response to the applied voltage is greatly reduced, and so is the tangential "surface conduction" in the diffuse layer, to the point that it can often be neglected compared to bulk conduction (small Dukhin number).

Loschmidt Echo in a System of Interacting Electrons

We study the Loschmidt echo for a system of electrons interacting through mean-field Coulomb forces. The electron gas is modeled by a self-consistent set of hydrodynamic equations. It is observed that the quantum fidelity drops abruptly after a time that is proportional to the logarithm of the perturbation amplitude. The fidelity drop is related to the breakdown of the symmetry properties of the wave function.

Correlated Brownian Motions as an Approximation to Deterministic Mean-Field Dynamics

We analyze the transition from deterministic mean-field dynamics of several large particles and infinitely many small particles to a stochastic motion of the large particles. In this transition the small particles become the random medium for the large particles, and the motion of the large particles becomes stochastic. Under the assumption that the empirical velocity distribution of the small particles is governed by a probability density ψ, the mean-field force can be represented as the negative gradient of a scaled version of ψ. The stochastic motion is described by a system of stochastic ordinary differential equations driven by Gaussian space-time white noise and the mean-field force as a shift-invariant integral kernel. The scaling preserves a small parameter in the transition, the so-called correlation length. In this set-up, the separate motion of each particle is a classical Brownian motion (Wiener process), but the joint motion is correlated through the mean-field force and the noise. Therefore, it is not Gaussian. The motion of two particles is analyzed in detail and a diffusion equation is deduced for the difference in the positions of the two particles. The diffusion coefficient in the latter equation is spatially dependent, which allows us to determine regions of attraction and repulsion of the two particles by computing the probability fluxes. The result is consistent with observations in the applied sciences, namely that Brownian particles get attracted to one another if the distance between them is smaller than a critical small parameter. In our case, this parameter is shown to be proportional to the aforementioned correlation length.

Two-body relaxation in modified Newtonian dynamics

A naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t 2b implies that t 2b is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of t 2b is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case, we find that in the deep-MOND regime t 2b scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Near the centre of a spherical system that is in the deep-MOND regime, we show that the fluctuating component of the gravitational force is never small compared to the mean-field force; this conclusion surprisingly even applies to systems with a density cusp that keeps the mean-field force constant to arbitrarily small radius, and suggests that a cuspy centre can never be in the deep-MOND regime. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two-body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ∼10 M ○. should have spiralled to the centres of dwarf galaxies.

Generalized multivariate Fokker–Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker–Planck equation. It is shown that this Fokker–Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions.

Properties of some collective excitations in spherical nuclei from the superheavy island

We study the β-vibrational spectrum of the putative double magic superheavy nucleus 292120, as predicted by the relativistic mean-field (RMF) model in a phenomenological collective approach and compare it with the one of the well-known double magic heavy nuclei 208Pb. Results are also presented for the elements 300120 and 298114. We use a selection of different mean-field forces and discuss their different predictions and the consequences for the collective modes.In the framework of the macroscopic model for giant resonances we compute the transition densities of the isoscalar monopole, quadrupole and octupole, and isovector dipole modes for the superheavy element 292120, whose ground state density is determined from the RMF model. The results are also compared to those of 208Pb.

Forces in the isotropic phase of a confined nematic liquid crystal 5CB.

Using a temperature controlled atomic force microscope, we have measured the temperature dependence of the force between a flat silanated glass surface and a silanated glass microsphere, immersed in the isotropic phase of the nematic liquid crystal 5CB (4'-n-pentyl 4-cyanobiphenyl). At separations of several nanometers, we observed a weak, short range attractive force of the order of 100 pN, which was increased by decreasing the temperature. The temperature dependence of the amplitude and the range of this attractive force can be described by a combination of van der Waals and a mean-field prenematic force due to the surface-induced nematic order. This is supported by ellipsometric study and allows for the determination of the surface coupling energy of 5CB on a silanated glass surface.

Casimir Interactions and Instability of Thin Nematic Films

We review our theoretical studies of mean-field and fluctuation-induced forces together with van der Waals force in a thin hybrid nematic film. We focus on the stability of nematic films frustrated by competing surface fields. Depending on temperature, anchoring strengths, and frustration, the films can be either stable, or they dewet the substrate through spinodal dewetting.

Adsorption of colloidal particles by Brownian dynamics simulation: Kinetics and surface structures

Careful control of the microstructure of an adsorbed monolayer of colloidal particles is important for creating nanostructured devices through self-assembly processes. We present a computational model study for self-assembly of colloidal or nanoscale particulate systems. We develop a new technique for simulating colloidal adsorption processes, and we examine the kinetics and the structure formation on the surface. The technique allows the simulation of a nonhomogeneous suspension with an open boundary that is in equilibrium with a bulk suspension of known volume fraction, including the mean-field forces from the bulk solution and particle flux between the simulation box and the bulk. Short-time kinetics follow a power law similar to the case of diffusion-limited adsorption. Long-time kinetics fit a 2/3-power law form [P. Schaaf, A. Johner, and J. Talbot, Phys. Rev. Lett. 66, 1603 (1991)] and kinetic coefficients are calculated. The zeta potential of the particles is the dominant parameter controlling the final surface coverage, but the zeta potential of the adsorbing surface is the dominant control for the ordering of the adsorbed system. Particles with larger Debye layers (lower salt concentrations) order more easily. Jamming limit coverages are compared to existing equivalent hard-disk models and an energetic model. Since the process is kinetically frustrated, particle exclusion effects play a major role in determining coverage as well as structure.

Lattice-boltzmann model for interacting amphiphilic fluids

We develop our recently proposed lattice-Boltzmann method for the nonequilibrium dynamics of amphiphilic fluids [H. Chen, B. M. Boghosian, P. V. Coveney, and M. Nekovee, Proc. R. Soc. London, Ser. A 456, 2043 (2000)]. Our method maintains an orientational degree of freedom for the amphiphilic species and models fluid interactions at a microscopic level by introducing self-consistent mean-field forces between the particles into the lattice-Boltzmann dynamics, in a way that is consistent with kinetic theory. We present the results of extensive simulations in two dimensions which demonstrate the ability of our model to capture the correct phenomenology of binary and ternary amphiphilic fluids.

Erratum: “Self-consistent mean-field forces in turbulent plasmas: Current and momentum relaxation” [Phys. Plasmas 5, 2257 (1998)

Erratum: “Self-consistent mean-field forces in turbulent plasmas: Current and momentum relaxation” [Phys. Plasmas <b>5</b>, 2257 (1998)

Self-consistent mean-field forces in turbulent plasmas: Current and momentum relaxation

The properties of turbulent plasmas are described using the two-fluid equations. Global constraints for the fluctuation-induced mean-field forces that act on the ion and electron fluids are derived. These constraints imply functional forms for the parallel mean-field forces in the Ohm’s law and the momentum balance equation. These forms suggest that the fluctuations attempt to relax the plasma to a state where both the current and the bulk plasma momentum are aligned along the mean magnetic field with proportionality constants that are global constants. Observations of flow profile evolution during discrete dynamo activity in reversed field pinch experiments are interpreted.

ON THE MEAN FIELD ANSATZ IN ANYON THEORIES

We study the physics of the mean field ansatz in a simplified anyon model. The model is solved exactly in a finite geometry with particular attention to boundary conditions compatible with a mean statistical magnetic field. The spectrum consists of bosonic plasma-like density fluctuations with a gap. We find that the repulsive Coulomb interactions introduced by the fluctuations around the mean field force the statistical charge and magnetic field to become localized near the boundaries. Translational invariance, broken by the mean field, is restored in the infinite volume limit as the statistical charge and magnetic field escape to infinity. The polarization effects of an external magnetic field and the role of “large” gauge transformations are also studied.

Theory of closed-loop liquid-liquid immiscibility in mixtures of molecules with directional attractive forces

The phase equilibria of a binary mixture of equal-sized hard spheres (diameters σ1 = σ2) with mean-field attractive forces between like species (a 11 = a 22) and non between unlike species (a 12 = 0) are determined using an ‘augmented’ van der Waals equation of state. This system is found to have a symmetrical phase diagram exhibiting a large extent of liquid-liquid immiscibility and a tricritical point. Directional attractive forces between the unlike species and then introduced in the form of off-centre, square-well bonding sites, and a perturbation term representing the contribution due to bonding is added to the equation of state. The phase behaviour of systems with varying degrees of association is investigated. As the strength of the site-site bonding interaction is increased relative to that of the mean-field attractions, closed-loop liquid-liquid immiscibility is found with the corresponding lower and upper critical solution points. The region of liquid-liquid coexistence decreases with increasing bonding strength until it disappears completely due to extensive association between the unlike species of the mixture. The fraction of bonded molecules is determined to provide an explanation of the phase behaviour; closed-loop immiscibility is a direct consequence of the dramatic increase in bonding as the temperature is decreased. Existing calculations for lattice models exhibiting closed-loop coexistence are discussed in the context of the results of this continuum approach, a first of its kind. Advantages of the approach in describing the properties of real systems exhibiting closed-loop immiscibility are pointed out.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean-field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self-consistently in the GSE. Analytic expressions for the wave-vector-dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function φ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave-vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l&amp;gt;1) of spherical dipolar molecules in a linearized theory. The expression of φ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave-vector-dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Water adsorption isotherms and hydration forces for lysolipids and diacyl phospholipids

The repulsive forces in a wide range of diacyl and monoacyl phospholipid systems have been obtained from the adsorption isotherms for water. From the exponential dependence of the repulsive pressure on the water content, information has been deduced regarding the hydration force. For diacyl phosphatidylcholines the strength of the hydration force and its characteristic decay length are in good agreement with values previously obtained by x-ray diffraction methods. For natural and synthetic diacyl phosphatidylcholines in the fluid lamellar phase, the hydration force extrapolated to zero layer separation (Po) is in the range 4-5.10(8) N.m-2 and the decay length is approximately 0.3 nm. The results for dimyristoyl, dipalmitoyl, and distearoyl phosphatidylcholines in the gel phase are very similar with Po approximately 2.5.10(8) N.m-2 and decay length of approximately 0.2 nm. Egg monomethyl phosphatidylethanolamine is less strongly hydrated: Po = 2.3.10(9) N.m-2, with a decay length of 0.3 nm. Egg phosphatidylethanolamine and bovine phosphatidylserine hydrate even more weakly with Po approximately 1.3.10(8) N.m-2 and decay length of approximately 0.15 nm. Mixtures with cholesterol or phosphatidylcholine increase both Po and the decay length for phosphatidylethanolamine to values closer to those for phosphatidylcholine. The repulsive forces deduced for egg lysophosphatidylcholine at 40 degrees C display a biphasic water dependence, with the low water phase being similar to lamellar egg phosphatidylcholine, and the phase at higher water content having a smaller value of Po = 2.10(8) N.m-2 but a longer decay length of approximately 0.45 nm, corresponding to a nonlamellar configuration. Bovine lysophosphatidylserine similarly yields values of PO = 1.2.108 N.m-2 and an effective decay length of 0.64 nm. The hydration behavior of the various diacyl phospholipids has been interpreted in terms of the mean-field molecular force theory of lipid hydration, and values deduced for the surface hydration potential of the various lipids. This analysis extends previous results on hydration forces, particularly to lysolipids and nonlamellar phases.

Functional Integrals in Stellar Dynamics

In the late 70s, the functional integral formulation equivalent to the Fokker-Planck equation was worked out (Graham). We apply this functional integral formulation to gravitationally interacting systems, whose dynamics may be analyzed by separating the forces operating on a particle into a mean field force and fluctuations due to random collisions at intermediate range (scattering at small angles). In this poster the formalism is presented for short periods (in the stochastical meaning) to systems with isotropic distribution background in velocity space (different spatial densities are possible). Later the functional integral for the local change for the distribution function is evaluated in the steepest descent approximation. In the end we point out the applicability of the method to slowly evolving globular star clusters near thermal equilibrium. In conditions of slow evolution we can express the evolution of the orbits in terms of local deviation from equilibrium.