Time-dependent Friction Research Articles

A cartilage-inspired lubrication system

Articular cartilage is an example of a highly efficacious water-based, natural lubrication system that is optimized to provide low friction and wear protection at both low and high loads and sliding velocities. One of the secrets of cartilage's superior tribology comes from a unique, multimodal lubrication strategy consisting of both a fluid pressurization mediated lubrication mechanism and a boundary lubrication mechanism supported by surface bound macromolecules. Using a reconstituted network of highly interconnected cellulose fibers and simple modification through the immobilization of polyelectrolytes, we have recreated many of the mechanical and chemical properties of cartilage and the cartilage lubrication system to produce a purely synthetic material system that exhibits some of the same lubrication mechanisms, time dependent friction response, and high wear resistance as natural cartilage tissue. Friction and wear studies demonstrate how the properties of the cellulose fiber network can be used to control and optimize the lubrication and wear resistance of the material surfaces and highlight what key features of cartilage should be duplicated in order to produce a cartilage-mimetic lubrication system.

Touch-down induced contact and friction forces at the dimple/gimbal interface

A dynamic simulation is performed to investigate contact and friction forces at the dimple/gimbal interface. The time history of slider motion, the resultant force as well as the pitch and roll moments acting on the slider are determined. The time-dependent contact and friction forces at the dimple/gimbal interface are obtained. The effect of material properties on contact and friction forces at the dimple/gimbal interface is investigated. Experimental results for touch-down and take-off characteristics are presented.

保存系支配方程式の高解像度スキームによる非定常層流圧力損失の高速高精度計算法

A highly accurate unified computation of transient response in pipelines is desirable in order to improve pneumatic components. This paper deals with a high resolution simulation of transient response in laminar pipe flow by solving the governing equations directly. The authors employed a TVD scheme for computation of its stable and less diffusive properties. To apply this scheme, the governing equations must be described for a conservative system. The time-dependent friction loss in laminar pipe flow, which had only been discussed for a non-conservative system, was therefore transformed into a conservative system and solved with the Chakravarthy-Osher TVD scheme. Computations for a pneumatic pipeline with several pipe diameters were performed. The computations for the developed method were compared with the standard CIP method, and showed higher resolution, more stable computation and shorter computation time than the CIP method. The developed method can be easily applied to turbulent or high-amplitude pipe flow by simply changing the friction term.

Frictional properties of olivine at high temperature with applications to the strength and dynamics of the oceanic lithosphere

Faulting and brittle deformation of mantle rocks occurs in many tectonic settings such as oceanic transform faults, oceanic detachment faults, subduction zones, and continental rifts. However, few data exist that directly explore the frictional properties of peridotite rocks. Improved constraints on the brittle deformation of peridotite is important for a more complete understanding of the rheological properties of the lithosphere. Furthermore, our comparatively detailed understanding of plastic deformation in olivine allows us to explore the possible role of thermally activated intracrystalline deformation mechanisms in macroscopically brittle processes. It has been hypothesized, and some experimental data indicate, that plastic yielding by dislocation glide (low temperature plasticity) determines the direct effect in the rate and state frictional constitutive formulation. Plastic flow may also have important implications for the blunting or necking at asperity contacts that influences the time and/or displacement dependent friction evolution effect and frictional healing. We present results from saw cut experiments on fine grained synthetic olivine fault gouge conducted in a gas‐medium deformation apparatus in the temperature range of 400–1000°C with 100 MPa confining pressure. We conducted velocity stepping tests to explore the rate and temperature dependence of sliding stability. We also conducted slide‐hold‐slide experiments to investigate the time and temperature dependence of fault zone restrengthening (frictional healing). The mechanical data and microstructural observations allow us to explore the role of thermally activated processes in frictional sliding. The data indicate systematic temperature dependenceof rate and state variables that can be attributed to plastic yielding at grain to grain contacts. We explore the implications of such temperature dependent behavior for controlling the base of the seismogenic zone in the oceanic lithosphere, and we seek insight into possible mechanistic models for the interactions between fracture and flow that could lead to improved constraints on the strength of the lithosphere.

Unifying model of driven polymer translocation

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to 10^{10} monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

Nonlinear electron transport in an electron-hole plasma

Charge transport in an electron-hole plasma driven by high-field terahertz (THz) pulses is strongly influenced by electron-hole interactions, as has been shown in a recent publication [P. Bowlan et al., Phys. Rev. Lett. 107, 256602 (2011)]. We introduce a picture of high-field THz transport which accounts for the roles of both types of carriers including their interactions. While holes make a negligible contribution to the current, they are heated by absorbing energy from the driving THz field and introduce a friction force for the electrons over a period of about 500 fs. Our model uses an extended version of the loss-function concept to calculate the time-dependent friction. The local field that drives the electrons differs from the incident THz field by screening due to Coulomb correlations in the plasma. We illustrate how spatial correlations between charged particles (electrons, holes, impurities) create a significant local-field correction to the THz driving field. The dominant contribution stems from Coulomb-correlated heavy-hole wave packets, which are strongly polarizable via inter-valence-band transitions.

High-Field Transport in an Electron-Hole Plasma: Transition from Ballistic to Drift Motion

The time evolution of high-field carrier transport in bulk GaAs is studied with intense femtosecond THz pulses. While ballistic transport of electrons occurs in an n-type sample, a transition from ballistic to driftlike motion is observed in an electron-hole plasma. This onset of friction is due to the holes, which are heated by THz absorption. Theoretical calculations, which reproduce the data quantitatively, show that both electron-hole scattering and local-field effects in the electron-hole plasma are essential for the time-dependent friction.

Nonlinear dissipative wave equations with space–time dependent potential

We study the long time behavior of solutions for damped wave equations with absorption. These equations are generally accepted as models of wave propagation in heterogeneous media with space–time dependent friction a ( t , x ) u t and nonlinear absorption | u | p − 1 u (Ikawa (2000) [17]). We consider 1 < p < ( n + 2 ) / ( n − 2 ) and separable a ( t , x ) = λ ( x ) η ( t ) with λ ( x ) ∼ ( 1 + | x | ) − α and η ( t ) ∼ ( 1 + t ) − β satisfying conditions (A1) or (A2) which are given. The main results are precise decay estimates for the energy, L 2 and L p + 1 norms of solutions. We also observe the following behavior: if α ∈ [ 0 , 1 ) , β ∈ ( − 1 , 1 ) and 0 < α + β < 1 , there are three different regions for the decay of solutions depending on p ; if α ∈ ( − ∞ , 0 ) and β ∈ ( − 1 , 1 ) , there are only two different regions for the decay of the solutions depending on p .

Transient Turbulent Flow and Heat Transfer Phenomena in Plate-Fin Type Cross-Flow Heat Exchanger

In this article, a transient performance of a plate-fin cross-flow heat exchanger with convergent–divergent longitudinal vortex generators is investigated. The effect of flow geometry is taken into account to analyze the transient forced convection heat transfer in a designed heat exchanger. The time-dependent Nusselt number and dissipation energy criterion are experimentally measured in 4- and 8-kW heater powers for various Reynolds numbers between 42,000 and 60,000 for the hot and cold fluids. In order to present the quality of the heat exchanger, the general empirical equations of the time-dependent Nusselt number and friction factor were derived as a function of the Reynolds number corresponding to fin geometry parameters. Following this, the transient behavior of the heat exchanger according to the change in the inlet and outlet temperatures of the hot and cold fluids was analyzed. The results showed that the variations of the time-dependent dissipation energy criterion increase with the increase in the Reynolds number. The appropriate correlations are proposed to predict the heat transfer and friction characteristics of the transient performance for the presented configuration, which indicates the designed heat exchanger has good heat conduction.

Application of Grote−Hynes Theory to the Reaction Catalyzed by Thymidylate Synthase

A theoretical study of dynamic effects on the rate-limiting step of the thymidylate synthase catalyzed reaction has been carried out by means of Grote-Hynes theory, successfully predicting the values of the recrossing effects for a chemical reaction that involves the transfer of a classical light particle. The transmission coefficients, obtained at 278, 293, 303, and 313 K, are almost invariant and in all cases far from unity, revealing a significant coupling of the environment motions and the reaction coordinate. Nevertheless, their energetic contribution to the activation free energy represents less than 0.50 kcal/mol for each of the four tested temperatures. Calculation of the transmission coefficient for the isotopically labeled hydride transfer has rendered almost the same values, in agreement with the experimentally observed temperature-independent KIEs. Fourier transform of the time-dependent friction kernel at these four temperatures has allowed obtaining the transition-state friction spectra, which present very small dependence with temperature. Their analysis has led to the identification of some key vibrational modes governing the coupling between the reaction coordinate and the protein environment, thus identifying the relevant motions in the active site and obtaining a full picture of the role of each amino acid.

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.

Friction of a Brownian Particle in a Lennard-Jones Solvent: A Molecular Dynamics Simulation Study

In this work, equilibrium molecular dynamics (MD) simulations in a microcanonical ensemble are performed to evaluate the friction coefficient of a Brownian particle (BP) in a Lennard-Jones (LJ) solvent. The friction coeffi-cients are determined from the time dependent friction coefficients and the momentum autocorrelation functions of the BP with its infinite mass at various ratios of LJ size parameters of the BP and solvent, σ

Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

We present coarse-grained molecular dynamics simulations of poly(ethylene-alt-propylene) (PEP) melts, ranging in chain length from about N(e) (the entanglement length) to N=6N(e). The coarse-grained parameters, potential of mean force and bare friction, were determined from fully atomistic molecular dynamics simulations carried out on a PEP cell containing 12 chains of 80 monomers each and subjected to periodic boundary conditions. These atomistic simulations were previously validated by means of extensive neutron scattering measurements. Uncrossability constrains were also introduced in the coarse-grained model to prevent unphysical bond crossing. The coarse-grained simulations were carried out at 492 K and focus on chain dynamics. The results obtained were analyzed in terms of Rouse coordinates and Rouse correlators. We observe deviations from Rouse behavior for all chain lengths investigated, even when the chain stiffness is incorporated in the Rouse model. These deviations become more important as the chain length increases. The general scenario emerging from the results obtained is that the deviations from Rouse-like behavior are due to correlations among the forces acting upon a chain bead, which seem to be related with the constraint of uncrossability among the chains. As consequence, nonexponentiality of the Rouse correlators and mode- and time-dependent friction are observed. It seems that, in the molecular weight explored, these effects still give not raise to reptation behavior but to a crossover regime between Rouse and reptation. On the other hand, the results obtained are in qualitative agreement with those expected from the so-called generalized Rouse models, based on memory function formalisms.

Colored noise, folding rates and departure from Kramers’ behavior

Recent experiments have shown that, for several proteins, the dependence of folding and unfolding rates on solvent viscosity does not obey Kramers' theory. Such a departure from standard Kramers' behavior is often attributed to the existence of internal friction, related to the structure of a polypeptide chain. In this paper, we propose an entirely different mechanism leading to violation of Kramers' theory. Using the generalized Langevin equation with time-dependent friction and a C(α)-Go model, we demonstrate that this effect may be caused by the colored Gaussian noise which is characterized by correlation time τ. Surprisingly, the dependence of folding time t(f) on τ is non-trivial: the plot t(f)vs τ exhibits two minima at low and intermediate values of τ. The appearance of one more additional minimum is in sharp contrast to one dimensional barrier crossing dynamics. We argue that it is a generic signature of entropy of activation in a multidimensional problem.

Influence of chondroitin sulfate on the biochemical, mechanical and frictional properties of cartilage explants in long-term culture

A recent study [Basalo et al., 2007. Chondroitin sulfate reduces the friction coefficient of articular cartilage. J. Biomech. 40(8), 1847–1854] has shown that the friction coefficient of bovine articular cartilage is reduced significantly by the supplementation of chondroitin sulfate (CS) at a concentration of 100 mg/ml. This result suggests that intra-articular injection of CS may be used as a prophylactic treatment against the progression of osteoarthritis. The objective of this study was to test the hypothesis that long-term culture of cartilage explants in CS produces no adverse mechanical, biochemical, or cytotoxic effects, while reducing the friction coefficient relative to the control group. Long-term cultures of live bovine articular cartilage explants were performed with incubation in media containing CS of three different concentrations (0, 10 and 100 mg/ml). Frictional tests (cartilage-on-glass) were performed under constant stress (0.5 MPa) for 3600 s and the time-dependent friction coefficient was measured. Samples incubated in a 100 mg/ml of CS solution exhibited a significantly lower equilibrium friction coefficient than the control (0.05±0.01 vs. 0.18±0.02 on Day 0, 0.04±0.01 vs. 0.14±0.04 on Day 7 and 0.04±0.01 vs. 0.15±0.06 on Day 14). Samples incubated in 10 mg/ml of CS did not exhibit any significant decrease in the friction coefficient. Cell viability and DNA content were maintained in all groups. However, after 28 days of culture, the Young's modulus and glycosaminoglycan content of explants incubated in 100 mg/ml of CS decreased to 5% and 40% of their initial levels, respectively. Based on this adverse outcome the hypothesis of this study is rejected, dampening our enthusiasm for the use of intra-articular CS injections as a prophylactic treatment in osteoarthritis.

Viscosity Scaling for the Glassy Phase of Protein Folding

Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.

The Signorini problem with Coulomb friction for a hyperelastic body under finite deformations

Abstract The quasi-static three-dimensional problem of elasticity theory for a hyperelastic body under finite deformations, loading by bulk and surface forces, partial fastening and unilateral contact with a rigid punch and in the presence of time-dependent anisotropic Coulomb friction is considered. The equivalent variational formulation contains a quasi-variational inequality. After time discretization and application of the iteration method, the problem arising with “specified” friction is reduced to a non-convex miniumum functional problem, which is studied by Ball's scheme. The operator in contact stress space is determined. It is shown that a threshold level of the coefficient of friction corresponds to each level of loading, below which there is at least one fixed point of the operator. If the solution at a certain instant of time is known, the iteration process converges to the solution of the problem at the next, fairly close instant of time.

Non-linear control of friction-induced self-excited vibration

The present paper introduces a new method of controlling friction-driven self-excited vibration. The control law is primarily derived using the Lyapunov's second method. A single degree-of-freedom oscillator on a moving belt represents the primary model of the system. The control action is achieved by modulating the normal load at the frictional interface based on the state of the oscillatory system. The basic mechanism of the control action utilises subcritical Hopf bifurcation of the equilibrium followed by cyclic-fold bifurcation (of limit cycle oscillations) to globally stabilise the equilibrium. The basic mechanism is qualitatively independent of the exact model of friction. Different models of friction, like, algebraic model, LuGre model and switch model with time-dependent static friction are considered to substantiate the above claim. An approximate method for estimating the critical value of the control parameter that ensures global stability of the equilibrium is also proposed.

Fluctuation-dissipation theorems in an expanding universe

The recently constructed minimal extension of the special relativistic Ornstein-Uhlenbeck process to curved space-time cannot be used to model realistically diffusions on cosmological scales because it does not take into account the evolution of the thermodynamical state of the matter with cosmological time. We therefore introduce a new class of non-minimal extensions characterized by time-dependent friction and noise coefficients. These new processes admit time-dependent Jüttner distributions as possible measures in momentum space; associated fluctuation-dissipation theorems are also proved and discussed.

1412 時間依存性摩擦則を用いたスティック・スリップ運動の安定性解析(OS14.衝撃・崩壊問題(2),ポスターセッションP-4)

1412 時間依存性摩擦則を用いたスティック・スリップ運動の安定性解析(OS14.衝撃・崩壊問題(2),ポスターセッションP-4)