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Nonequilibrium energy dissipation at the interface of sliding model hydroxylated alpha-alumina surfaces.

Nonequilibrium molecular dynamics simulations were performed to study the dynamics of energy transfer at the interface of a small nanoscale hydroxylated alpha-alumina surface sliding across a much larger surface of the same material. Sliding velocities of 0.05, 0.5, 5, and 50 ms and loads of 0, 0.0625, 5, 15, 25, and 100 nN were considered. Nonequilibrium energy distributions were found at the interface for each of these conditions. The velocity distribution P(v) for the atoms in a sublayer of the smaller surface oscillates during the sliding, reflecting the periodicity of the interfacial intermolecular potential. When averaged over the sliding, this P(v) for each of the sublayers is bimodal with Boltzmann and non-Boltzmann components. The non-Boltzmann component, with temperatures in excess of 1000 K and as high as 2500 K, is most important for the interfacial H-atom sublayer and becomes less important in moving to a sublayer further from the interface. Similarly, the temperature of the Boltzmann component decreases for sublayers further from the interface and approaches the 300 K temperature of the boundary. The temperature of the Boltzmann component decreases, but the importance of the non-Boltzmann component increases, as the sliding velocity is decreased. The temperature of the non-Boltzmann component is relatively insensitive to the sliding velocity. Friction forces are determined by calculating the energy dissipation during the sliding, and different regimes are found for variation in the friction force versus sliding velocity v(s) and applied load. For v(s) of 0.05, 0.5, and 5 ms, the friction force is inversely proportional to v(s) reflecting the increased time for energy dissipation as v(s) is decreased.

Journal Article↗

Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems.

We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.

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An idealized model for nonequilibrium dynamics in molecular systems.

The nonequilibrium dynamics of highly nonlinear and multidimensional systems can give rise to emergent chemical behavior which can often be tracked using low-dimensional order parameters such as a reaction path. Such behavior cannot be readily surmised by stationary projected stochastic representations such as those described by the Langevin equation or the generalized Langevin equation (GLE). The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with space-dependent friction. For more general forms of the friction kernel, the iGLE was previously shown to be the projection of a mechanical system with a time-dependent Hamiltonian [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)]. In the present work, the corresponding open Hamiltonian system is shown to be amenable to numerical integration despite the presence of a nonlocal term. Simulations of this mechanical system further confirm that the time dependence of the observed total energy and the correlations of the solvent force are in precise agreement with the projected iGLE. This extended nonstationary Hamiltonian is thus amenable to the study of nonequilibrium bounds and fluctuation theorems.

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Elastic properties of swollen polyelectrolyte gels in aqueous salt solutions.

The elastic relaxation responding to a uniaxially stretched poly(acrylic acid) rodlike gel in the aqueous NaCl solution was investigated. The relaxation elucidated the shear (mu) and bulk (K) moduli and the frictional coefficients (sigma) of the fully ionized gel at pH above 9 as functions of the degree of swelling, which was controlled by the NaCl concentration (C(S)) of the solution. Two gels, cross-linked chains of which consist of 500 (GelA500) and 50 (GelA50) monomeric units, were examined to investigate the effect of the chain length on the elastic behavior. The moduli of GelA500 increased with swelling at C(S) below 100 mM and decreased at C(S) above it. The mu values of both gels can be characterized by the power function of gel diameter, d as mu proportional, variantd(beta). The beta values being -1 at C(S) above 100 mM transitionally changed to 1.2 at C(S) about 100 mM. That is, the dimensionality of space for the chains to distribute, n(dim) [= (beta+5)/(beta+2) according to the conventional theory [Sasaki et al., J. Chem. Phys. 102, 5694 (1995)]], changed from 4 (n(dim) of ideal chain) to 1.9 at C(S) = 100 mM. This indicates that the electrostatic repulsion between gel chains reduces the n(dim) at C(S) below 100 mM but not at C(S) above it. It was found that the K values of GelA500 were well described by the conventional theory but those of GelA50 not. The sigma(zr)/sigma(rr) (sigma(zr) is an off-diagonal element of the friction coefficient tensor and sigma(rr) is a diagonal element of the friction coefficient tensor) was found to be 2.7 x 10(-2), which was the same as the previously reported value for the swollen poly(acrylamide) gel [Sasaki, J. Chem. Phys. 120, 5789 (2004)]. The sigma(rr) of unit volume of the GelA500 is well explained by the free draining model while the sigma(rr) of GelA50 is less than that of the free draining model, suggesting the slip between water and ionized chain.

Absorption↗

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study.

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.

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Slip complexity in dynamic models of earthquake faults.

We summarize recent evidence that models of earthquake faults with dynamically unstable friction laws but no externally imposed heterogeneities can exhibit slip complexity. Two models are described here. The first is a one-dimensional model with velocity-weakening stick-slip friction; the second is a two-dimensional elastodynamic model with slip-weakening friction. Both exhibit small-event complexity and chaotic sequences of large characteristic events. The large events in both models are composed of Heaton pulses. We argue that the key ingredients of these models are reasonably accurate representations of the properties of real faults.

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Thermodynamic and hydrodynamic properties of human tropoelastin. Analytical ultracentrifuge and pulsed field-gradient spin-echo NMR studies.

Tropoelastin is the soluble precursor of elastin that bestows tissue elasticity in vertebrates. Tropoelastin is soluble at 20 degrees C in phosphate-buffered saline, pH 7.4, but at 37 degrees C equilibrium is established between soluble protein and insoluble coacervate. Sedimentation equilibrium studies performed before (20 degrees C) and after (37 degrees C) coacervation showed that the soluble component was strictly monomeric. Sedimentation velocity experiments revealed that at both temperatures soluble tropoelastin exists as two independently sedimenting monomeric species present in approximately equal concentrations. Species 1 had a frictional ratio at both temperatures of approximately 2.2, suggesting a very highly expanded or asymmetric protein. Species 2 displayed a frictional ratio at 20 degrees C of 1.4 that increased to 1.7 at 37 degrees C, indicating a compact and symmetrical conformation that expanded or became asymmetric at the higher temperature. The slow interconversion of the two monomeric species contrasts with the rapid and reversible process of coacervation suggesting both efficiently incorporate into the coacervate. A hydrated protein of equivalent molecular weight modeled as a sphere and a flexible chain was predicted to have a frictional ratio of 1.2 and 1.6, respectively. Tropoelastin appeared as a single species when studied by pulsed field-gradient spin-echo NMR, but computer modeling showed that the method was insensitive to the presence of two species of equal concentration having similar diffusion coefficients. Scintillation proximity assays using radiolabeled tropoelastin and sedimentation analysis showed that the coacervation at 37 degrees C was a highly cooperative monomer-n-mer self-association. A critical concentration of 3.4 g/liter was obtained when the coacervate was modeled as a helical polymer formed from the monomers via oligomeric intermediates.

Humans↗

Contributions and co-ordination of individual fingers in multiple finger prehension.

The contributions and co-ordination of external finger grip forces were examined during a lifting task with a precision grip using multiple fingers. The subjects (n = 10) lifted a force transducer-equipped grip apparatus. Grip force from each of the five fingers was continuously measured under different object weight (200 g, 400 g and 800 g) and surface structure (plastic and sandpaper) conditions. The effect of five-, four-, and three-finger grip modes was also examined. It was found that variation of object weight or surface friction resulted in change of the total grip force magnitude; the largest change in finger force, was that for the index finger, followed by the middle, ring, and little fingers. Percentage contribution of static grip force to the total grip force for the index, middle, ring, and little fingers was 42.0%, 27.4%, 17.6% and 12.9%, respectively. These values were fairly constant for all object weight conditions, as well as for all surface friction conditions, suggesting that all individual finger force adjustments for light loads less than 800 g are controlled comprehensively simply by using a single common scaling value. A higher surface friction provided faster lifting initiation and required lesser grip force exertion, indicating advantageous effect of a non-slippery surface over a slippery surface. The results indicate that nearly 40% force reduction can be obtained when a non-slippery surface is used. Variation in grip mode changed the total grip force, i.e., the fewer the number of fingers, the greater the total grip force. The percent value of static grip force for the index, middle, and ring fingers in the four-finger grip mode was 42.7%, 32.5%, and 24.7%, respectively, and that for the index and middle fingers in the three-finger grip mode was 43.0% and 56.9%, respectively. Therefore, the grip mode was found to influence the force contributions of the middle and ring fingers, but not of the index finger.

Adolescent↗

Age-related changes in grip force and dynamics of hand movement.

The authors investigated whether older adults (n = 16; mean age = 65 years) increased grip force to compensate for load force fluctuations during up and down movements more than young adults did (n = 16; mean age = 24 years) and whether older and young adults exhibited similar adaptation of grip force to alterations in friction associated with changes in object surface texture. As previously reported, older adults used a higher level of grip force than young adults during static holding. Increased grip force was observed in the older group during movement. The increase was appropriate to the lower coefficient of friction estimated for the older group. In both groups, grip force was greater with a smooth than with a rough surface (the latter having the higher coefficient of friction) during static holding and during movement. Moreover, grip force modulation was equally well synchronized with load force fluctuation during movement in the two groups. The authors concluded that changes in organization of grip force with age are well adapted to change in hand-object interface properties. Elevated grip force in older adults does not necessarily signify a fundamental change in synchronizing grip force modulation with load force fluctuation.

Adolescent↗

Dynamics of double stranded DNA reptation from bacteriophage.

The dynamics of dsDNA release process from a phage head has been analyzed theoretically. The process was considered as dsDNA reptation through the phage tail. The driving force is assumed to be the decrease of the DNA globule free energy on its releasing from the head in the surrounding medium. The results of the equilibrium theory on an intraphage DNA globule were applied. Three possible sources of friction were examined. The first one is in the inner channel of the tail. The second is the friction of DNA segments in the whole globule volume, which is essential when the globule decondensation is a collective process, at simultaneous moving of all the turns (mechanism 1). The third is the globule friction with the capsid inner surface, that is most important when decondensation proceeds via the globule rotation as a whole spool (mechanism 2). Mechanism 1 would require a lot of time for ejection. Mechanism 2 would lead to different ejection dynamics of short- and long-tailed phages. Comparison of the theoretical results with the published experimental data argues in favor of mechanism 2.

Bacteriophages↗

The transport of salt and water across isolated rat ileum. Evidence for at least two distinct pathways.

The flows of sodium, potassium, and chloride under electrical and chemical gradients and of salt and water in the presence of osmotic pressure gradients are described by phenomenological equations based on the thermodynamics of irreversible processes. The aim was to give the simplest possible description, that is to postulate the least number of active transport processes and the least number of separate pathways across the intestine. On this basis, the results were consistent with the following picture of the intestine: Two channels exist across this tissue, one allowing only passive transport of ions and the other only active. In the passive channel, the predominant resistance to ion flow is friction with the water in the channel. The electroosmotic flow indicates that the passive channel is lined with negative fixed charged groups having a surface charge density of 3000 esu cm-2. The values of the ion-water frictional coefficients, and the relationship between ionic concentrations and flows indicate that the passive channel is extracellular. The active channel behaves as two membranes in series, the first membrane being semipermeable but allowing active transport of sodium, and the second membrane being similar to the passive channel. Friction with the ions in the second "membrane" is the predominant resistance to water flow.

Animals↗

The counterface, surface smoothness, tolerances, and coatings in total joint prostheses.

Proper counterface material combinations, surface finish, and tolerances of contact surfaces are important issues in minimizing friction, wear, and corrosion of total joint prostheses. In the current study, the potential of novel amorphous diamond coatings to solve some present problems in total joint prostheses was studied by using tribological tests with a hip joint simulator and pin-on-disk testers. Based on the tests, the wear of amorphous diamond is negligible compared with conventional hip joint materials (10,000 to 1,000,000 times lower). The coefficient of friction of diamond-coated artificial hip joint was 0.03 to 0.06 when tested in saline solution with loads from 200 to 1000 kg for as many as two million cycles. The friction remained stable throughout the tests. Methylmethacrylate (bone cement) is a typical source of third body wear particles in cemented total hip replacements. The wear tests showed that bone cement (containing hard ceramic particles of barium sulfate or zirconia) severely scratched cobalt chromium molybdenum alloy samples. These scratches enhance the wear of softer counterpart materials, such as polyethylene or bone cement, whereas diamond-coated surfaces remained undamaged. High quality amorphous diamond coatings offer superior stability (minimal wear debris release in surrounding tissues) and good biomechanical performance.

Acetabulum↗

Power law mass dependence of diffusion: A mode coupling theory analysis

The self-diffusion coefficient of a tagged molecule is known to exhibit a weak mass dependence, especially for solutes with size comparable to or larger than the size of the solvent molecules. Sometimes this mass dependence can be fitted to a power law, with a small exponent, less than 0.1. This weak mass dependence has often been considered as supportive of the hydrodynamic picture (that is, the Stokes-Einstein relation) of diffusion rather than the kinetic theory approach, which predicts a stronger mass dependence, for example, via the Enskog theory. Neither can explain the weak power-law mass dependence. In order to understand this, we have carried out a mode coupling theory (MCT) analysis of diffusion. It is found that a straightforward application of the existing mode coupling theory expressions lead to an inaccurate mass dependence-it predicts an increase of diffusion coefficient with an increase of the mass. We find that this is because of the inadequate description of the initial decay of the collective contributions to the friction. We have proposed a new prescription to accurately describe the short time dynamics of the density and the current term. In addition, we have modified the existing MCT by imposing the full self-consistency between the frequency-dependent friction and the mean square displacement over the whole time and frequency plane. Previously the self-consistency was performed only at the zero frequency level between the zero frequency friction and the diffusion coefficient. With these two generalizations, the mode coupling theory is found to provide a fairly accurate description of the mass dependence. In particular, the theory can correctly reproduce the power-law dependence of solvent-solute diffusion ratio on solute-solvent mass ratio, observed in computer simulations of Bearman and Jolly [Mol. Phys. 44, 665 (1981)]. Another important result is that the current mode is found to play no significant role in determining the diffusion. Thus the hydrodynamic argument of weak mass dependence has little validity for same size solute-solvent systems.

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Velocity space scattering coefficients with applications in antihydrogen recombination studies

An approach for calculating velocity space friction and diffusion coefficients with Maxwellian field particles is developed based on a kernel function derived in a previous paper [Y. Chang and C. A. Ordonez, Phys. Plasmas 6, 2947 (1999)]. The original fivefold integral expressions for the coefficients are reduced to onefold integrals, which can be used for any value of the Coulomb logarithm. The onefold integrals can be further reduced to standard analytical expressions by using a weak coupling approximation. The integral expression for the friction coefficient is used to predict a time scale that describes the rate at which a reflecting antiproton beam slows down within a positron plasma, while both species are simultaneously confined by a nested Penning trap. The time scale is used to consider the possibility of achieving antihydrogen recombination within the trap. The friction and diffusion coefficients are then used to derive an expression for calculating the energy transfer rate between antiprotons and positrons. The expression is employed to illustrate achieving antihydrogen recombination while taking into account positron heating by the antiprotons. The effect of the presence of an electric field on recombination is discussed.

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Dynamic phase transitions in confined lubricant fluids under shear.

A surface force apparatus was used to measure the transient and steady-state friction forces between molecularly smooth mica surfaces confining thin films of squalane, C30H62, a saturated, branched hydrocarbon liquid. The dynamic friction "phase diagram" was determined under different shearing conditions, especially the transitions between stick-slip and smooth sliding "states" that exhibited a chaotic stick-slip regime. The apparently very different friction traces exhibited by simple spherical, linear, and branched hydrocarbon films under shear are shown to be due to the much longer relaxation times and characteristic length scales associated with transitions from rest to steady-state sliding, and vice versa, in the case of branched liquids. The physical reasons and tribological implications for the different types of transitions observed with spherical, linear, and branched fluids are discussed.

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Numerical investigation of the angle of repose of monosized spheres.

This paper presents a numerical study of the angle of repose, a most important macroscopic parameter in characterizing granular materials, by means of a modified distinct element method. Emphasis is given to the effect of variables related to factors such as particle characteristics, material properties, and geometrical constraints. The results show that sliding and rolling frictions are the primary reasons for the formation of a sandpile; particle size and container thickness significantly influence the angle of repose; and the angle of repose is not so sensitive to density, Poisson's ratio, damping coefficient, and Young's modulus. Increasing rolling friction coefficient or sliding friction coefficient increases the angle of repose. Conversely, increasing particle size or container thickness decreases the angle of repose. The underlying mechanisms for these effects are discussed in terms of particle-particle and particle-wall interactions.

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Discrete Burridge-Knopoff model, with exact solitonic or compactlike traveling wave solution.

We have explored the dynamics of two versions of a Burridge-Knopoff model: with linear or nonlinear interactions between adjacent blocks. We have shown that by properly choosing the analytical form of the discrete solitary wave solution of the model we can calculate analytically the form of the friction function. In both cases our analytical results show that the friction force naturally presents the behavior of a simple weakening friction law first introduced qualitatively by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 3411 (1967)] and quantitatively by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989)]. With such a force function the discrete solitonic or compactlike wave-front solutions are exact and stable solutions. In the case of linear coupling our numerical simulations show that an irregular initial state evolves into kink pairs (large-amplitude events), that can recombine or not, plus nonlinear localized modes and small linear oscillations (small-amplitude events) that disperse with time, owing to dispersion. For nonlinear coupling one observes compactlike kink pairs or shocks, and a background of robust incoherent nonlinear oscillations (small amplitude events) that persist with time. Our results show that discreteness is a necessary ingredient to observe a rich and complex dynamical behavior. Nonlinearity allows the existence of strictly localized shocks.

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Transition regimes for growing crack populations.

Numerous observational papers on crack populations in the material and geological sciences suggest that cracks evolve in such a way as to organize in specific patterns. However, very little is known about how and why the self-organization comes about. We use a model of tensile-like cracks with friction in order to study the time and space evolution of normal faults. The premise of this spring-block analog is that one could model crustal deformation for long time scales assuming a brittle layer coupled to a ductile substrate. The long time-scale physics incorporated into the model are slip-weakening friction, strain-hardening rheology for coupling the two layers, and randomly distributed yield strength of the brittle layer. We investigate how the evolution of populations of cracks depends on these three effects, using linear stability analysis to calculate the stable regimes for the friction as well as numerical simulations to model the nonlinear interactions of the cracks. We find that we can scale the problem to reduce the relevant parameters to a single one, the slip weakening. We show that the distribution of lengths of active cracks makes a transition from an exponential at very low strains, where crack nucleation prevails, to a power law at low to intermediate strains, where crack growth prevails, to an exponential distribution of the largest cracks at higher strains, where coalescence dominates. There is evidence of these different length distributions in continental and oceanic normal faults. For continental deformation the strain is low, and the faults have power-law frequency-size distributions. For mid-ocean ridge flanks the strain is greater, up to an order of magnitude higher than the continental strain, and faults have exponential-like frequency-size distributions. No theory has been offered to explain this difference in the distributions of continental and mid-ocean faults. In this paper we argue that they are indicative of different stages of evolution. The former faults are at an early stage of relatively small deformation, while the latter are at a later stage of the evolution. For high strain the faults reach a saturation regime with system size cracks evenly spaced in proportion to the brittle layer thickness. We asymptotically approximate the time space evolution of faults as a long time-scale phenomenon, thereby avoiding modeling the short time-scale earthquakes. We show that this assumption is valid, which implies that the faults that creep and faults with earthquakes display the same time and space evolutions.

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