System Of Hard Disks Research Articles

Mode-coupling analysis of residual stresses in colloidal glasses.

We present results from computer simulation and mode-coupling theory of the glass transition for the nonequilibrium relaxation of stresses in a colloidal glass former after the cessation of shear flow. In the ideal glass, persistent residual stresses are found that depend on the flow history. The partial decay of stresses from the steady state to this residual stress is governed by the previous shear rate. We rationalize this observation in a schematic model of mode-coupling theory. The results from Brownian-dynamics simulations of a glassy two-dimensional hard-disk system are in qualitative agreement with the predictions of the theory.

Crystallization induced by multiple seeds: Dynamical density functional approach

Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.

Direct measurement of osmotic pressure via adaptive confinement of quasi hard disc colloids

Confining a system in a small volume profoundly alters its behaviour. Hitherto, attention has focused on static confinement where the confining wall is fixed such as in porous media. However, adaptive confinement where the wall responds to the interior has clear relevance in biological systems. Here we investigate this phenomenon with a colloidal system of quasi hard discs confined by a ring of particles trapped in holographic optical tweezers, which form a flexible elastic wall. This elasticity leads to quasi-isobaric conditions within the confined region. By measuring the displacement of the tweezed particles, we obtain the radial osmotic pressure. We further find a novel bistable state of a hexagonal structure and concentrically layered fluid mimicking the shape of the confinement. The hexagonal configurations are found at lower pressure than those of the fluid, thus the bistability is driven by the higher entropy of disordered arrangements, unlike bulk hard systems.

Massively parallel Monte Carlo for many-particle simulations on GPUs

Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little attention because of the inherent serial nature of the statistical sampling. In this paper, we present a massively parallel method that obeys detailed balance and implement it for a system of hard disks on the GPU. We reproduce results of serial high-precision Monte Carlo runs to verify the method. This is a good test case because the hard disk equation of state over the range where the liquid transforms into the solid is particularly sensitive to small deviations away from the balance conditions. On a Tesla K20, our GPU implementation executes over one billion trial moves per second, which is 148 times faster than on a single Intel Xeon E5540 CPU core, enables 27 times better performance per dollar, and cuts energy usage by a factor of 13. With this improved performance we are able to calculate the equation of state for systems of up to one million hard disks. These large system sizes are required in order to probe the nature of the melting transition, which has been debated for the last forty years. In this paper we present the details of our computational method, and discuss the thermodynamics of hard disks separately in a companion paper.

Orthogonal versus covariant Lyapunov vectors for rough hard disc systems

The Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this paper, the covariant Lyapunov vectors, the orthogonal Gram–Schmidt vectors and the corresponding local (time-dependent) Lyapunov exponents are analyzed for a planar system of rough hard discs (RHDS). These results are compared to respective results for a smooth-hard-disc system (SHDS). We find that the rotation of the discs deeply affects the Oseledec splitting and the structure of the tangent space. For both the smooth and rough hard discs, the stable, unstable and central manifolds are transverse to each other, although the minimal angle between the unstable and stable manifolds of the RHDS typically is very small. Both systems are hyperbolic. However, the central manifold is precisely orthogonal to the rest of the tangent space only for the smooth-particle case and not for the rough discs. We also demonstrate that the rotations destroy the Hamiltonian (symplectic) character for the RHDS.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.

Triple-Stage-Actuator System of Head-Positioning Control in Hard Disk Drives

In this paper, we propose a triple-stage actuator system with a thermal actuator to increase a servo bandwidth of a head-positioning control system in hard disk drives. The thermal actuator is good for control in high frequency range because it has little negative impact caused by mechanical resonances. Therefore, the proposed system with a thermal actuator can control the head position beyond the major mechanical resonances caused by a voice coil motor (VCM) or piezoelectric (PZT) actuator. As a result, the servo bandwidth of the proposed triple-stage actuator system can be higher than that of the conventional dual-stage actuator system which consists of the VCM and the PZT actuators. Simulation results of sensitivity functions showed that the disturbance-compensation performance below 2 kHz will be improved by 6 dB with proposed control system.

Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods

We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.

Inherent structure landscape connection between liquids, granular materials, and the jamming phase diagram.

We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system of hard disks confined to a narrow channel. The J line is shown to be divided into packings that are either accessible or inaccessible from the equilibrium fluid. The J point itself is found to occur at the transition between these two sets of packings and is located at the maximum of the inherent structure distribution. We also present a general thermodynamic argument that suggests the density of the states at the maximum of the configurational entropy represents a lower bound on the J-point density in hard sphere systems. Finally, we show that the granular system, modeled using the Edwards ensemble, and the fluid sample the same set of thermodynamically accessible states over the full range of thermodynamic state points, but only occupy the same set of inherent structures, under the same thermodynamic conditions, at two points, corresponding to zero and infinite pressures, where they sample the J-point states and the most dense packing, respectively.

Development of Optimized Adaptive Feed-Forward Cancellation with Damping Function for Head Positioning System in Hard Disk Drives

This paper presents an adaptive feed-forward cancellation (AFC) technique with a damping function based on optimized AFC. The proposed AFC includes a mechanical resonance characteristic as an internal model that is realized by using the damping function and that achieves the best performance in the frequency domain. This makes it possible to apply the proposed AFC to suppress not only repeatable run-out (RRO) but also non-repeatable run-out (NRRO) of the head positioning system in hard disk drives. Simulation results showed that the proposed AFC can suppress NRRO such as disk flutter vibration and that the stability of the feedback loop was improved by the damping function.

The Discrete-Time Sliding Mode Control with Computation Time Delay for Repeatable Run-Out Compensation of Hard Disk Drives

The presented is a study on the problem of disturbance rejection, specifically the periodic disturbance, by applying discrete-time sliding mode control method. For perturbations such as modeling errors and external disturbances, their compensation is formulated using the designed sliding mode control. To eliminate the effect of these perturbations, the convergence rate between the disturbance and their compensation has been shaped by an additional parameter. Decoupling of the resultant perturbation estimation dynamics from the closed loop dynamics is achieved. Computation time delay is also presented to address the perturbation effects. The approach developed ensures the robustness of the sliding mode dynamics to parameter uncertainties and exogenous disturbances, in addition to the complete rejection of the periodic disturbance component. Satisfactory simulation results as well as experimental ones have been achieved based on a fast servo system of a modern hard disk drive to illustrate the validity of the controller for repeatable run-out (RRO) compensation.

Transport coefficients in the $2$-dimensional Boltzmann equation

We show that a rarefied system of hard disks in a plane, described in the Boltzmann-Grad limit by the $2$-dimensional Boltzmann equation, has bounded transport coefficients. This is proved by showing opportune compactness properties of the gain part of the linearized Boltzmann operator.

Improvement of Convergence for Adaptive Feed-Forward Cancellation Using Variable Gains in a Head Positioning System of Hard Disk Drives

AbstractWe present an enhanced adaptive feed-forward cancellation (AFC) with variable gainsto be used in the head positioning control system of a hard disk drive (HDD). Thevariable gains can help to improve the convergence characteristic of the enhanced AFCafter the track seeking control. Therefore, the proposed enhanced AFC can improvethe transient response of the head positioning after the track seeking control. Thetrack seeking simulation results from HDDs showed that the proposed control methodcompensated for the disturbances caused by the repeatable run-out (RRO) and airflow-induced vibration immediately after the track seeking control.Key words 1. Introduction The rapid growth in demand for a larger data capacity requires an increase in the arealdensity of hard disk drives (HDDs). The head positioning control system of an HDD mustcompensate for any disturbances, because increasing the track density requires improvingthe head positioning accuracy in the head positioning control system of an HDD

Fragile-Strong Fluid Crossover and Universal Relaxation Times in a Confined Hard-Disk Fluid

We show that a system of hard disks confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adam-Gibbs relation does not predict the relaxation behavior. We also show that a facilitated dynamics description of the system, where kinetically excited regions are identified with local packing arrangements of the disks, successfully describes the fragile-strong crossover.

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D~(φ(c)-φ(m))(μ-β) for all values of the polydispersity, where φ(m) is the area fraction and φ(c) is the value of φ(m) at the percolation threshold.

An electro-thermal micro-actuator based on polymer composite for application to dual-stage positioning systems of hard disk drives

This paper presents an electro-thermal micro-actuator based on polymer composite for dual-stage head positioning systems in hard disk drives (HDDs). This micro-actuator has a pair of benders, which are made of silicon–polymer composite. When electro-thermally activated by resistive heating, the composite expands and consequently the benders produce a lateral bending motion to drive a femto slider, which carries a magnetic read/write head. The micro-actuator has been fabricated by deep silicon etching and polymer patterning. Experiment shows that the micro-actuator can drive up to 35nm peak-to-peak displacement when it is activated by a 3.25V half-sine input voltage at 500Hz under a moderate temperature rise. The first in-plane mechanical resonant frequency is measured to occur at 36.8kHz. Analytical and finite element models were developed to simulate the micro-actuator performance. It is noted that the simulation results agree well with the experimental measurement. With good performance, the electro-thermal micro-actuator are useful for high bandwidth dual-stage positioning systems in future high-density HDDs.

Optimization of adaptive feedforward repeatable run-out cancellation for positioning control system of hard disk drives

To increase the recording density of hard disk drives, suppression of the disturbances is essential. In this paper, we focus on the suppression of repeatable run-out. This paper presents the design method of an adaptive feedforward cancellation (AFC) which can suppress a periodic disturbance. AFC is adaptive filter. The algorithm can be converted into a linear time-invariant (LTI) model. The LTI model is considered to be a peak filter for a closed loop system. Therefore, parameters of AFC should be designed in consideration of a closed loop characteristics. The proposed method can design the parameters that can achieve a vector locus to recede from the critical point [− 1, 0] on the Nyquist diagram. As a result, convergence performances and stability performances of AFC are optimized in frequency domain. The effectiveness of the proposed method is verified by the simulations and experiment of the hard disk drive.

Deterministic Thermal Reservoirs

We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism for hard disks where the collision rule at the boundary is modified. Numerical evidence and theoretical argument is given that suggests that an energy balance is achieved for a system of hard disks in contact with two reservoirs at equal temperatures. This system however produces entropy near the the system-reservoir boundaries and this entropy flows into the two reservoirs. Thus rather than producing an equilibrium state, the system is at a steady state with a steady entropy flow without any associated energy flux. The microscopic mechanisms associated with energy and entropy fluxes for this system are examined in detail.

Localization properties of covariant Lyapunov vectors for quasi-one-dimensional hard disks

The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant vectors and the localization properties of both Gram-Schmidt and covariant vectors. At low density there is a kinetic regime that has simple scaling properties for the Lyapunov exponents and the average localization for part of the spectrum. This regime shows strong localization in a proportion of the first Gram-Schmidt and covariant vectors and this can be understood as highly localized configurations dominating the vector. The distribution of angles between neighboring covariant vectors has characteristic shapes depending upon the difference in vector number, which vary over the continuous region of the spectrum. At dense gas- or liquid-like densities the behavior of the covariant vectors are quite different. The possibility of tangencies between different components of the unstable manifold and between the stable and unstable manifolds is explored but it appears that exact tangencies do not occur for a generic chaotic trajectory.

Elasticity of two-dimensional crystals of polydisperse hard disks near close packing: Surprising behavior of the Poisson's ratio

The equation of state, elastic constants, and Poisson's ratio of a crystalline two-dimensional polydisperse hard disk system were determined in the close packing limit. Monte Carlo simulations in the NpT ensemble with variable shape of the periodic box reveal that the pressure and elastic constants grow with increasing polydispersity. The equation of state and the bulk modulus are well described by the free volume approximation. The latter approximation fails, however, for the shear modulus. The simulations also show that the introduction of any amount of size polydispersity in the hard disk systems causes a discontinuous "jump" of the Poisson's ratio in the close packing limit from the value ν(δ=0) = 0.1308(22), obtained for equidiameter hard disks, to ν(δ>0) ≈ 1, estimated for the polydisperse disks.

Free-energy landscape for cage breaking of three hard disks

We investigate cage breaking in dense hard-disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free-energy landscape containing two energy minima separated by an energy barrier. The exact free-energy landscape can be calculated as a function of system size by a direct enumeration of states. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of using a one-dimensional representation to understand dynamics through a multidimensional space, such as diffusion acquiring spatial dependence and discontinuities in spatial derivatives of free energy.