Biomedical subjects

Phil Attard

Publications and source records attributed to Phil Attard.

17 recordsLinked to original sources

PubMed2006

Statistical mechanical theory for steady state systems. VI. Variational principles.

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

Journal Article↗

PubMed2006

Theory for non-equilibrium statistical mechanics.

This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life.

Algorithms↗

PubMed2006

Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density.

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.

Journal Article↗

PubMed2006

Statistical mechanical theory for steady state systems. IV. Transition probability and simulation algorithm demonstrated for heat flow.

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results.

Journal Article↗

PubMed2005

Effects of degassing on the long-range attractive force between hydrophobic surfaces in water.

The long-ranged attractions between hydrophobic amorphous fluoropolymer surfaces are measured in water with and without dissolved air. An atomic force microscope is used to obtain more than 500 measured jump-in distances, which yields statistically reliable results. It is found that the range of the attraction and its variability is generally significantly decreased in deaerated water as compared to normal, aerated water. However, the range and strength of the attraction in deaerated water remain significantly greater than the van der Waals attraction for this system. The experimental observations are consistent with (1) nanobubbles being primarily responsible for the long-ranged attraction in normal water, (2) nanobubbles not being present in deaerated water when the surfaces are not in contact, and (3) the attraction in the absence of nanobubbles being most probably due to the approach to the separation-induced spinodal cavitation of the type identified by Bérard et al. [J. Chem. Phys. 1993, 98, 7236]. It is argued that the measurements in deaerated water reveal the bare or pristine hydrophobic attraction unobscured by nanobubbles.

Polymers↗

PubMed2005

Surface tension of a Lennard-Jones liquid under supersaturation.

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.

Algorithms↗

PubMed2005

Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid.

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green-Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green-Kubo expression. An ansatz for the steady-state probability distribution for heat flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is found to be accurate in the high-density regime at not too short times, but not more generally. The probability distribution is implemented in Monte Carlo simulations, and a method for extracting the thermal conductivity is given.

Journal Article↗

PubMed2005

A random walk through the dynamics of homogeneous vapor-liquid nucleation.

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.

Journal Article↗

PubMed2005

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

Journal Article↗

PubMed2005

Stabilization of native protein fold by intein-mediated covalent cyclization.

A mutant version of the N-terminal domain of Escherichia coli DnaB helicase was used as a model system to assess the stabilization against unfolding gained by covalent cyclization. Cyclization was achieved in vivo by formation of an amide bond between the N and C termini with the help of a split mini-intein. Linear and circular proteins were constructed to be identical in amino acid sequence. Mutagenesis of Phe102 to Glu rendered the protein monomeric even at high concentration. A difference in free energy of unfolding, DeltaDeltaG, between circular and linear protein of 2.3(+/-0.5) kcal mol(-1) was measured at 10 degrees C by circular dichroism. A theoretical estimate of the difference in conformational entropy of linear and circular random chains in a three-dimensional cubic lattice model predicted DeltaDeltaG=2.3 kcal mol(-1), suggesting that stabilization by protein cyclization is driven by the reduced conformational entropy of the unfolded state. Amide-proton exchange rates measured by NMR spectroscopy and mass spectrometry showed a uniform, approximately tenfold decrease of the exchange rates of the most slowly exchanging amide protons, demonstrating that cyclization globally decreases the unfolding rate of the protein. The amide proton exchange was found to follow EX1 kinetics at near-neutral pH, in agreement with an unusually slow refolding rate of less than 4 min(-1) measured by stopped-flow circular dichroism. The linear and circular proteins differed more in their unfolding than in their folding rates. Global unfolding of the N-terminal domain of E.coli DnaB is thus promoted strongly by spatial separation of the N and C termini, whereas their proximity is much less important for folding.

Adenosine Triphosphatases↗

PubMed2004

Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient.

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them.

Journal Article↗

PubMed2004

Molecular dynamics study of the effect of atomic roughness on the slip length at the fluid-solid boundary during shear flow.

A systematic study into the effect of solid roughness on the slip boundary condition during shear flow is presented. Atomic roughness is modeled by varying the size and spacing between solid atoms at constant packing fraction while the interaction parameters and the thermodynamic state of the fluid are kept constant. It is shown that the fluid structure as manifest in the amplitude of the density oscillations increases with increasing smoothness of the surfaces. The fluid-solid slip length is shown to exhibit nonmonotonic behavior as the solid structure is varied from smooth to rough. Slip occurs for both smooth and rough surfaces, and stick occurs only for surfaces commensurate with the fluid.

Journal Article↗

PubMed2004

Monte Carlo simulation methodology of the ghost interface theory for the planar surface tension.

A novel "ghost interface" expression for the surface tension of a planar liquid-vapor interface is derived in detail from consideration of the free energy of the system, and a methodology for utilization of this new technique is given. An augmented Monte Carlo computer simulation procedure is developed specifically for the ghost interface, including derivation of long-range corrections resulting from potential truncation and a modified Gibbs ensemble technique for the simulation of adjacent coexisting phases. Results generated from the ghost interface theory for the surface tension are presented and found to be in good quantitative agreement with those resulting from the Kirkwood-Buff equation. Applications of this new approach to curved and to supersaturated systems are also discussed.

Journal Article↗

PubMed2003

Curvature-dependent surface tension of a growing droplet.

A ghost interface simulation technique is developed and applied to supersaturated Lennard-Jones liquid-vapor interfaces. It is shown that the surface tension decreases approximately linearly with the supersaturation ratio and that it vanishes at the spinodal. The effect leads to a curvature-dependent surface tension since, it is argued, the local supersaturation of the vapor above a droplet is greater than in the bulk due to slow diffusion in the vapor phase. An analytic approximation is given for the local supersaturation ratio, and an analytic expression for this contribution to Tolman's length is derived. The theory gives a smaller critical radius and reduces the free energy barrier to nucleation compared to classical homogeneous nucleation theory, which have important implications for the kinetics of droplet and bubble formation.

Journal Article↗

PubMed2003

Nanobubbles and the hydrophobic attraction.

The evidence for nanobubbles as the origin of the long-ranged attractions measured between hydrophobic surfaces immersed in water is reviewed by focusing upon several unique features of the force curves. Also covered is the morphology of nanobubbles as revealed by direct imaging with tapping mode atomic force microscopy. A discussion of the origin, thermodynamic stability and practical implications of nanobubbles is given.

Biophysical Phenomena↗

PubMed2002

Constraint method for deriving nonequilibrium molecular dynamics equations of motion.

A procedure for developing non-Hamiltonian equations of motion for constrained systems is given. It is shown that such constraints can be used to mimic common statistical systems, both equilibrium (e.g., constant temperature) and nonequilibrium (e.g., shear flow, heat flow), and the procedure is suited for molecular dynamics computer simulations. The method is demonstrated with isokinetic shear flow, in bulk and slit geometries, which illustrates its flexibility. Results for the shear viscosity are in agreement with previously published results.

Journal Article↗

PubMed2002

Effective spring description of a bubble or a droplet interacting with a particle.

It is shown that the interaction of a particle with a liquid drop or a gas bubble may be quantitatively described over the whole distance regime by treating the fluid interface as a Hookean spring. An algorithm suitable for analyzing atomic force microscopy data suitable for a calculator or a spread-sheet is given and applied to data for oil drops.

Letter↗