Dissipative Work Research Articles

Dynamic force spectroscopy of DNA hairpins: II. Irreversibility and dissipation

We investigate irreversibility and dissipation in single molecules that cooperativelyfold/unfold in a two-state manner under the action of mechanical force. We apply paththermodynamics to derive analytical expressions for the average dissipated work and theaverage hopping number in two-state systems. It is shown how these quantities only dependon two parameters that characterize the folding/unfolding kinetics of the molecule: thefragility and the coexistence hopping rate. The latter has to be rescaled to take intoaccount the appropriate experimental set-up. Finally we carry out pulling experimentswith optical tweezers in a specifically designed DNA hairpin that shows two-statecooperative folding. We then use these experimental results to validate our theoreticalpredictions.

The cooperative effect of a colloidal particle driven by a periodic signal in a harmonic potential

For a colloidal particle in a harmonic potential driven by a periodic signal，we study its thermodynamic behavior and obtain the exact expressions of the effective temperature and dissipated work by solving the corresponding Langevin equation. The results show that due to the cooperative effect of the potential，the signal and the noise，the energy of the environment can be transferred to the colloidal particle through the stirring action of the periodic driving force，which makes the effective temperature of the system increase greatly. Under the condition of dynamical resonance，the dissipated work also reaches its maximum.

Nonequilibrium fluctuation-dissipation theorem of Brownian dynamics.

Studying the Brownian motion of a system driven by an external control from one macroscopic state to another macroscopic state, this paper presents the derivation of a nonlinear fluctuation-dissipation theorem (FDT). The new FDT relates the nonequilibrium work to the equilibrium free-energy difference in a very simple manner. It is valid wherever the Brownian dynamics is applicable. It recovers the well-known Crooks fluctuation theorem (CFT) within the quasiequilibrium regime where the dissipative work is nearly zero. It will also be shown that the CFT's fundamental assumption of microscopic reversibility is not obeyed in experiments such as mechanically unfolding biological molecules, in which the external driving forces depend on the system's coordinates.

Protein-Protein Interaction Investigated by Steered Molecular Dynamics: The TCR-pMHC Complex

We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.

Structural Damping with Friction Beams

In the last several years, there has been increasing interest in the use of friction joints for enhancing damping in structures. The joints themselves are responsible for the major part of the energy dissipation in assembled structures. The dissipated work in a joint depends on both the applied normal force and the excitation force. For the case of a constant amplitude excitation force, there is an optimal normal force which maximizes the damping. A ‘passive’ approach would be employed in this instance. In most cases however, the excitation force, as well as the interface parameters such as the friction coefficient, normal pressure distribution, etc., are not constant. In these cases, a ‘semi-active’ approach, which implements an active varying normal force, is necessary. For the ‘passive’ and ‘semi-active’ approaches, the normal force has to be measured. Interestingly, since the normal force in a friction joint influences the local stiffness, the natural frequencies of the assembled structure can be tuned by adjusting the normal force. Experiments and simulations are performed for a simple laboratory structure consisting of two superposed beams with friction in the interface. Numerical simulation of the friction interface requires non-linear models. The response of the double beam system is simulated using a numerical algorithm programmed inMATLABwhich models point-to-point friction with the Masing friction model. Numerical predictions and measurements of the double beam free vibration response are compared. A practical application is then described, in which a friction beam is used to damp the vibrations of the work piece table on a milling machine. The increased damping of the table reduces vibration amplitudes, which in turn results in enhanced surface quality of the machined parts, reduction in machine tool wear, and potentially higher feed rates. Optimal positioning of the friction beams is based on knowledge of the mode shapes, which are obtained from experimental modal analysis. The modal damping and the natural frequencies for the two dominant modes are measured for several combinations of excitation force and normal force.

Mechanical and energetical analysis of molecular dynamics simulations of dislocation–defect interactions

In this paper, we present a method of analysis on the continuum scale of molecular dynamics simulations of dislocation–defect interactions. It is shown how the applied work can be decomposed into its elementary components: the elastic strain energy, the dissipated work against the Peierls stress and the curvature energy needed to enable the dislocation, pinned by the defect, to bow out. While the dissipated work is entirely extracted from the system in molecular statics, the elastic and curvature energies contribute to a large increase in the internal energy. The curvature energy is evaluated and compared with predictions of the line tension model. This analysis allows the calculation of the dislocation–defect interaction energy and the determination of the predominant features in the unpinning process.

Investigation of Inhomogeneous Deformation on Meso-Scale with Crystal Plasticity Finite Element

The influence of crystallographic orientation stability on the inhomogeneous deformation on the meso-scale was numerically simulated with the crystal plasticity finite element. The initial microstructures were introduced into the finite element via intra-granular orientation gradient. The results demonstrated that the average orientation for both stable Goss and meta-stable cube oriented grains changed very little in plane strain compression (PSC). And for stable Goss oriented grain, the orientation gradient increased slightly, but for meta-stable cube oriented grain, the orientation gradient increased dramatically. And in spite of the same Taylor factor for both oriented grains, the dissipated averaged energy for cube oriented grain was higher than for Goss oriented grains, and the distribution width of dissipated work in cube oriented grain was also wider than that in Goss oriented grain. Furthermore, there was also strong energy gradient in PSC of cube oriented grain. Both the orientation gradient and energy gradient favor the nucleation of cube grains during recrystallization.

A non‐linear programming method approach for upper bound limit analysis

AbstractThis paper presents a finite element model based on mathematical non‐linear programming in order to determine upper bounds of colapse loads of a mechanical structure.The proposed formulation is derived within a kinematical approach framework, employing two simultaneous and independent field approximations for the velocity and strain rate fields. The augmented Lagrangian is used to establish the compatibility between these two fields. In this model, only continuous velocity fields are used.Uzawa's minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate. The use of this technique allows to bypass the complexity of the non‐linear aspects of the problem, since non‐linearity is addressed as a set of small local subproblems of optimization for each finite element.The obtained model is quite versatile and suitable for solving a wide range of collapse problems. This paper studies 3D strut‐and‐tie structures, 2D plane strain/stress and 3D solid problems. Copyright © 2007 John Wiley & Sons, Ltd.

Some studies on rotors with polynomial type non-linear external and internal damping

Non-linear internal damping in rotating cylindrical shafts leads to isotropic non-linear circulatory and dissipative force fields. Orbital instability in such class of systems arises when the regenerative work due to circulatory forces exceeds the dissipative work done over an orbit. In this paper, stability condition for rotor shafts with polynomial type non-linear internal damping is derived and also it is shown that distortion of the critical orbit, which results in larger change in orbital path as compared to the change in enclosed area, may lead to stable orbit at normally unstable operating conditions. This principle is applied to stabilize a simple rotor with discontinuous stiffness characteristics, which come into effect on exceeding some threshold displacement of the rotor itself.

Fluctuation symmetries for work and heat

We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time dependence is specified by an external protocol. We give conditions on potential and protocol under which the fluctuations of the dissipative work satisfy an exact symmetry for all times. We also present counterexamples to that fluctuation theorem when our conditions are not satisfied. Finally, we consider the dissipated heat, which differs from the work by a temporal boundary term. We explain why there is a correction to the standard fluctuation theorem due to the unboundedness of that temporal boundary. However, the corrected fluctuation relation has again a general validity.

An Investigation into the Physics Behind the Stabilizing Effects of Two-Phase Lubricants in Journal Bearings

Solid phase particles in two-phase lubricants used in journal bearings undergo deformation in the bearing clearance space during large amplitude journal whirl. The orbital energy causing instability of the rotor shaft is drawn from the drive and it is proportional to the orbital area whereas energy dissipation offered by the fluid film is a path function. The balance of these two energies decides the stability of rotor-bearing system. In the first part of this paper, equivalent snubber springs have been used to represent contact with solid phase particles and purely elastic collision is modeled. It is analytically shown that any perturbation of a circular orbit increases dissipative work, which may entrain the response of an otherwise unstable system (i.e., without perturbation) to a stable orbit. In the second part of this paper, a rigid rotor supported on journal bearings using two-phase lubricants is studied and it is shown that discontinuity in the support forces arising out of contact with solid-phase particles, irrespective of the nature of deformation of particles, is responsible for controlling the whirl orbit size.

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [Phys. Rev. E 61, 2361 (2000)] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work W(d) in the F and R pullings is the same, (ii) both U(z) and W(d) can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W(d). To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.

Thermodynamic solutions for equilibrium beach profiles

Solutions are developed for beach profiles using equilibrium principles of thermodynamics applied to simple representations of the nearshore fluid dynamics. Equilibrium beaches are posed as isothermal shorezone systems of constant volume that dissipate external work by incident waves into heat given up to the surroundings. By the maximum entropy production formulation of the second law of thermodynamics (the law of entropy increase), the shorezone system achieves equilibrium with profile shapes that maximize the rate of dissipative work performed by wave‐induced shear stresses. Dissipative work is assigned to two different shear stress mechanisms prevailing in separate regions of the shorezone system, an outer solution referred to as the shorerise and a bar‐berm inner solution. The equilibrium shorerise solution extends from closure depth (zero profile change) to the breakpoint, and maximizes dissipation due to the rate of working by bottom friction. In contrast, the equilibrium bar‐berm solution between the breakpoint and the berm crest maximizes dissipation due to work by internal stresses of a turbulent surf zone. Both shorerise and bar‐berm equilibria were found to have an exact general solution belonging to the class of elliptic cycloids. The elliptic cycloid allows all significant features of the equilibrium profile to be characterized by the eccentricity and the size of the ellipse axes. These basic ellipse parameters are evaluated by process‐based algorithms and empirically validated parameters for which an extensive literature already exists. The elliptic cycloid solutions displayed wave height, period and grain size dependence and demonstrate generally good predictive skill in point‐by‐point comparisons with measured profiles.

Work distribution functions for hysteresis loops in a single-spin system

We compute the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. Using Glauber dynamics we perform Monte Carlo simulations to find the work distributions at different driving rates. We find that in general the work distributions are broad with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates are studied analytically. We verify that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.

Experimental test of Hatano and Sasa's nonequilibrium steady-state equality.

Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. & Paniconi, M. (1998) Prog. Theor. Phys. Suppl. 130, 29-44] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. & Sasa, S. (2001) Phys. Rev. Lett. 86, 3463-3466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of Y, a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, -ln<e(-Y)> = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that -ln<e(-Y)> approximately 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.

Equilibrium free energies from path sampling of nonequilibrium trajectories

Jarzynski’s relation between equilibrium free energy and nonequilibrium work is rewritten as an average of work with respect to a work weighted ensemble. The present form is more appropriate for computer application of Jarzynski’s relation where the dissipative work is frequently much greater than kBT. Monte Carlo sampling of very short nonequilibrium trajectories yields good estimates of the equilibrium free energy change. The procedure can be thought of as a generalization of thermodynamic integration in ordinary free energy calculations. Very short trajectories can be used to compute the free energy difference. In the infinitely short trajectory limit, we recover the thermodynamic integration scheme. We also show that free energy estimate can be obtained from moments of the work distribution. The last result is most useful for experimental measurements of the free energy.

Classical and Statistical Thermodynamics. Ashley H. Carter

This book provides a solid introduction to the classical and statistical theories of thermodynamics (http://vig.prenhall.com/catalog/academic/product/1,4096,0137792085,00.html).[...]

A two-state kinetic model for the unfolding of single molecules by mechanical force.

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate) and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results. We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within k(B)T, from nonequilibrium experiments by using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, W(dis) to k(B)T.

The impact of work input to sorption cycles

In recent years the interest in cooling machines or heat pumps combining the principles of compression and sorption technology is increasing. The reason is that both technologies have specific drawbacks which can be overcome by the combination. Our discussion is centred around absorption cycles which use a compressor, and, consequently, an input of a significant amount of mechanical work in addition to heat. In most publications cycles of this kind are discussed in terms of one single COP as usual in the refrigeration industry. This, however, is wrong from a thermodynamic, and misleading from a technical and economical point of view. In order to highlight the need for a strict thermodynamic approach, a fundamental difference between distinct kinds of work input, namely “recoverable work”, “dissipative work” and “heat transformation work” is discussed in the first part of the paper. In the second part it is shown how the input of both work and heat into a energy conversion system has to be handled with both mechanical and thermal COP. The method is thermodynamically sound and straightforward, technically feasible and easy to apply, and most quickly transferred into economical terms. In the third part, a practical example of a compression–absorption hybrid is investigated.

ENERGY ANALYSIS OF A NONLINEAR MODEL OF THE NORMAL HUMAN LUNG

Despite the existence of respiratory mechanics models in the literature, rarely one finds analytical expressions that predict the work of breathing (WOB) associated with natural breathing maneuvers in non-ventilated subjects. In the present study, we develop relations that explicitly identify WOB, based on a proposed nonlinear model of respiratory mechanics. The model partitions airways resistance into three components (upper, middle and small), includes a collapsible airways segment, a viscoelastic element describing lung tissue dynamics and a static chest wall compliance. The individual contribution of these respiratory components on WOB is identified and analyzed. For instance, according to model predictions, during the forced vital capacity (FVC) maneuver, most of the work is expended against dissipative forces, mainly during expiration. In addition, expiratory dissipative work during FVC is almost equally partitioned among the upper airways and the collapsible airways resistances. The former expends work at the beginning of expiration, the latter at the end of expiration. The contribution of the peripheral airways is small. Our predictions are validated against laboratory data collected from volunteer subjects and using the esophageal catheter balloon technique.