System Of Hard Disks Research Articles

Microscopic mechanisms of diffusion dynamics: A comparative efficiency study of event-chain Monte Carlo variants in dense hard disk systems.

In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at equilibrium, comparing novel methodologies of event-chain Monte Carlo variants, specifically the Newtonian event-chain and straight event-chain algorithms. We systematically analyze both event-based and CPU time-based efficiency in liquid and solid phases, aiming to elucidate the microscopic mechanisms underlying structural relaxation. Our results demonstrate how chain length or duration, system size, and phase state influence the efficiency of diffusion dynamics, including hopping motion. This work provides insights into optimizing simulation techniques for highly packed systems and has the potential to improve our understanding of diffusion dynamics even in complex many-body systems.

Anomalous flocking in nonpolar granular Brownian vibrators

Using Brownian vibrators, we investigated the structures and dynamics of quasi-2d granular materials, with packing fractions (ϕ) ranging from 0.111 to 0.832. Our observations revealed a remarkable large-scale flocking behavior in hard granular disk systems, encompassing four distinct phases: granular fluid, flocking fluid, poly-crystal, and crystal. Anomalous flocking emerges at ϕ = 0.317, coinciding with a peak in local density fluctuations, and ceased at ϕ = 0.713 as the system transitioned into a poly-crystal state. The poly-crystal and crystal phases resembled equilibrium hard disks, while the granular and flocking fluids differed significantly from equilibrium systems and previous experiments involving uniformly driven spheres. This disparity suggests that collective motion arises from a competition controlled by volume fraction, involving an active force and an effective attractive interaction resulting from inelastic particle collisions. Remarkably, these findings align with recent theoretical research on the flocking motion of spherical active particles without alignment mechanisms.

On the equation of state of the hard disk system: the fluid-hexatic phase transition

The accuracy of four approximations proposed along time as equations of state for a homogeneous system of hard disks is compared against molecular dynamics results of 10 5 disks in equilibrium [L. Mier-y-Terán, J. Munguía and J. Antonio Moreno-Razo, Mol. Phys. (2023). doi:10.1080/00268976.2023.2288702]. Three of the equations studied here are Padé approximants. Only one of the approximations studied, based on the virial expansion of the compressibility factor of the homogeneous fluid, is considered to have sound physical grounds. Assuming that the total pressure predicted generates the positional part of the Helmholtz free energy, only, the four approximations, combined with the molecular dynamics simulation results referred above, allow identifying four linear regions, where different orientational processes can be associated with the well known steps of the melting transition. Results for a finite system are consistent with the KTHNY theory. In particular, under this assumption, the four approximations, with small quantitative differences, show the ordering effects present in the fluid at the low-density-end of the fluid-hexatic first-order phase transition. It is shown that the latter region continues to exist under the assumption proposed. In addition, a linear combination of the virial and compressibility coefficients is used to obtain a more accurate version of the Carnahan-Starling type approximation for the hard-disk system.

Simple and efficient methods for local structural analysis in polydisperse hard disk systems.

In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular jamming transitions and various aspects of the behavior of active matter. However, conventional techniques (based on a fixed-distance cutoff or the Voronoi construction) have mainly been applied to equilibrated, homogeneous, and monodisperse particle systems. In this paper, we implement simple and efficient methods for local structure analysis in nonequilibrium, inhomogeneous, and polydisperse hard disk systems. We show how these novel methods can overcome the difficulties encountered by conventional techniques as well as demonstrate some applications.

Study of the positional and orientational contributions to the Helmholtz free energy of a finite hard-disk system. A molecular dynamics analysis of its hexatic transition

Based on an equilibrium thermodynamic scheme, this work studies the separation of the Helmholtz free energy of a hard-disk system into its positional and orientational contributions. For the positional part, an accurate two dimensional version of the Carnahan-Starling equation of state is proposed, while a simple ansatz of the one particle partition function for the orientational part is proposed. The latter expression, which contains information about the probability of the norm of the six-fold orientational order parameter, is obtained through molecular dynamics simulations. Perhaps due to finite size effects, the ordering of the fluid is not a sudden phenomenon: the fluid-hexatic phase transition is preceded by a linear increase in the orientational contribution to the pressure of the fluid. A similar result is obtained for the hexatic-solid phase transition. Thus, the hexatic first-order phase transition is located between two linear ordering processes, consistent with the KTHNY theory. The proposed separation also predicts the existence of first order fluid-hexatic phase transition by using two procedures: the first, based on a purely bimodal probability density function, produces a pressure with a van del Waals-like first-order phase transition, while the second, considering density fluctuations, results in a flattened pressure phase transition.

Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks Pergamenshchik [19] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density Nd/L where d is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at Nd/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. Comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed.

Geometric conjecture about phase transitions.

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach the steady state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and ε-mixing time of the configuration spaces of hard-disk and hard-sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems and numerical evidence suggests that a discontinuity in the ε-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.

ASIC Implementation of Nonlinear CNN-Based Data Detector for TDMR System in 28 nm CMOS at 200 Mbits/s Throughput

In this work, we present the first application-specific integrated circuit (ASIC) implementation of a convolutional neural network (CNN)-based data detection channel for the two-dimensional magnetic recording (TDMR) system in hard disk drive (HDD). This chip is fabricated in TSMC 28 nm complementary metal–oxide–semiconductor (CMOS). TDMR signals captured from a real HDD are used to train and test the network, and the chip is designed to make inferences only. This work presents a systematic pipeline to codesign the neural network structure and the corresponding hardware implementation. To meet the high-throughput requirement, the CNN is fully unrolled with dedicated silicon for each convolution layer using systolic arrays. Quantization-aware training algorithms are used to help improve power efficiency without comprising accuracy. Overall, our chip achieves 200 Mbits/s throughput at 0.9 V supply voltage. In addition, it achieves improved detection accuracy compared to the physical-model-based conventional channel. Our chip consumes 173–219 mW power at 200 M3 clock rate for supply voltage 0.8–0.9 V, respectively.

Erratum: ``Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system'' [Condens. Matter Phys., 2023, 26, 33501: 1-12, DOI:10.5488/CMP.26.33501

Erratum: ``Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system'' [Condens. Matter Phys., 2023, 26, 33501: 1-12, DOI:10.5488/CMP.26.33501

Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system

The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory incorporates both contributions, and their sum is shown to determine the free volume and partition function. The approach is based on multiple intersections of the circles concentric with the disks but of twice larger radius. The result is exact formulae for the extensive and intensive entropy contributions in terms of the intersections of just two, three, four, and five circles. The method has an important advantage for applications in numerical simulations: the formulae enable one to convert the disk coordinates into the entropy contribution directly without any additional geometric construction. The theory can be straightforwardly applied to a system of hard spheres.

Brownian motion in a growing population of ballistic particles.

We investigate the motility of a growing population of cells in a idealized setting: We consider a system of hard disks in which new particles are added according to prescribed growth kinetics, thereby dynamically changing the number density. As a result, the expected Brownian motion of the hard disks is modified. We compute the density-dependent friction of the hard disks and insert it in an effective Langevin equationto describe the system, assuming that the intercollision time is smaller than the timescale of the growth. We find that the effective Langevin description captures the changes in motility, in agreement with the simulation results. Our framework can be extended to other systems in which the transport coefficient varies with time.

Diffusional characteristics of a Newtonian event-chain Monte Carlo in hard disk systems

The equilibration and relaxation times of the physical properties of time correlation functions have historically been of fundamental importance in terms of molecular simulation. An efficient algorithm for the acceleration of equilibration, termed the ‘event-chain Monte Carlo’ has been investigated over the past decade. Recently, by adding the collision rule often used in event-driven molecular dynamics, a Newtonian event-chain Monte Carlo was developed. In this event-chain Monte Carlo and variants thereof, optimal performance strongly depends on chain length, physical properties, and system size; the microscopic mechanism in play remains elusive. To identify key factors affecting equilibration, we investigated the diffusional characteristics per event (collision) for each algorithm, focusing systematically on the diffusion coefficients and pair dispersions in two-dimensional hard disk systems.

High-bandwidth controller design for dual-stage actuator system in hard disk drives

Large-capacity hard disk drives are important for the development of an information society. The capacities of hard disk drives depend on the positioning accuracy of magnetic heads, which read and write digital data, in disk-positioning control systems. Therefore, it is necessary to improve positioning accuracy to develop hard disk drives with large capacities. Hard disk drives employ dual-stage actuator systems to accurately control the magnetic heads. A dual-stage actuator system consists of a voice coil motor and micro-actuator. In micro-actuators, there is a trade-off between head-positioning accuracy and stroke limitation. In particular, in a conventional controller design, the micro-actuator is required to actuate such that it compensates for low-frequency vibration. To overcome this trade-off, this study proposes a high-bandwidth controller design for the micro-actuator in a dual-stage actuator system. The proposed method can reduce the required stroke of the micro-actuator by increasing the gain of the feedback controller of the voice coil motor at low frequencies. Although the voice coil motor control loop becomes unstable, the micro-actuator stabilizes the entire feedback loop at high frequencies. As a result, the control system improves the positioning accuracy compared to that achieved by conventional control methods, and the required micro-actuator stroke is reduced.

A Case Study of Network Mobility (NEMO-BSP) Integration with Leo Constellation System

Introduction: This manuscript is explicating the mutual compatibility of boot modes in a computer system and partition-ing styles of Hard Disk Drive. Most of us are familiar with these terms and know a little about these. Method: This manuscript contains the ample information about the boot modes of a computer system and partitioning styles of Hard Disk Drive (HDD) and their related configuration through which we get to know about their configuration and endurability. It also contains some practically verified case studies of the problems which occur due to the wrong con-figuration of boot modes and partitioning styles, though there are lot more but the most common ones are discussed along with their solutions. Result: In order to achieve the compatibility, it might require to convert the primary HDD into either GPT or MBR parti-tioning schemes. It should be marked that this interconversion wipes data on HDD, so cautiously the data on the hard drive must be backed-up before any conversion process. Conclusion: The information contained had been practically verified and is helpful in coping with the newer technology trends which contains more features along with backward compatibility. Keywords: Mobile IPv4, Mobile IPv6, NEMO, QoS, NS-2. Discussion: Right now passengers of flight are forced to interact with flight’s pre-recorded entertainment system. Most of the passenger airlines do not allow a passenger to use the internet or any other type of interaction with the ground while during the flight. They force passengers to even switch their mobile to FLIGHT MODE so that there is no active commu-nication between a passenger and the remaining world.

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis.

Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) restitution. After a formally exact linear stability analysis of the Navier-Stokes-Fourier hydrodynamic equations in terms of the translational (d_{t}) and rotational (d_{r}) degrees of freedom, the transport coefficients derived in the companion paper [A. Megías and A. Santos, "Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients" Phys. Rev. E 104, 034901 (2021)10.1103/PhysRevE.104.034901] are employed. Known results for hard spheres [Garzó, Santos, and Kremer, Phys. Rev. E 97, 052901 (2018)10.1103/PhysRevE.97.052901] are recovered by setting d_{t}=d_{r}=3, while novel results for hard disks (d_{t}=2,d_{r}=1) are obtained. In the latter case, a high-inelasticity peculiar region in the (α,β) parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for dilute systems of hard disks at α=0.2 shows that this theoretical region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a shrinking of the conditions for stability. In the case of moderate inelasticity (α=0.7), however, a good agreement between the theoretical predictions and the simulation results is found.

Compatibility Study of Installation of an Operating System with Boot Modes and Partitioning Styles Configuration

Introduction: This manuscript is explicating the mutual compatibility of boot modes in a computer system and partitioning styles of Hard Disk Drive. Most of us are familiar with these terms and know a little about these. Methods: This manuscript contains ample information about the boot modes of a computer system and partitioning styles of Hard Disk Drive (HDD) and their related configuration through which we get to know about their configuration and endurability. It also contains some practically verified case studies of the problems which occur due to the wrong configuration of boot modes and partitioning styles, though there are a lot more, the most common ones are discussed along with their solutions. Result: In order to achieve the compatibility, it might require to convert the primary HDD into either GPT or MBR partitioning schemes. It should be marked that this interconversion wipes data on HDD, so cautiously the data on the hard drive must be backed-up before any conversion process. Discussion: This is helpful when the system is equipped with the latest configuration, i.e., UEFI, and if there is a need to install an older operating system that does not support UEFI boot mode (for example, Windows XP), then CSM can help. In addition, some graphics cards (for example, GTX 680) do not support UEFI and hence, require CSM to boot. This means that the CSM can help as a runner for all that hardware configuration (in an updated system with new configuration), which can run only through legacy BIOS configuration. Conclusion: The information contained had been practically verified and is helpful in coping with the newer technology trends which contains more features along with backward compatibility.

Reply to “Comment on ‘Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system’ ”

There is indeed a finite-size issue in computer simulations of the correlation decay in a quasi-one-dimensional system of hard disks. The correlation function obtained from the exact canonical $NVT$ partition function shows a decay which is much slower and more complex than the exponential one, presented in the Comment.

Collective Dynamics in Quasi-One-Dimensional Hard Disk System

We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel. The computer simulations have been performed for the specific channel width of 3/2 of disk diameter in which the disk arrangement at close packing resembles zigzag ordering characteristic of a vertically oriented two-dimensional (2D) triangular lattice. In such a quasi-1D system, which is intermediate between 1D and 2D arrays of hard disks, the transverse excitations obey very specific dispersion law typical of the usual optical transverse modes. This is in a sharp contrast both to the 1D case, where transverse excitations are not possible, and to the 2D case, where the regular shear waves with a propagation gap were observed. Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of hard disk densities typical for fluid and distorted crystal states.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features.

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

Global equation of state and the phase transitions of the hard disc system

The hard disc system plays a fundamental role in the study of two-dimensional matters. High-precision compressibility data and a complete picture of the phase transitions have been reported for all the phases and phase transition regions for the hard disc system with numerical simulation results. However, thorough descriptions of the system and phase transitions depend on analytical equations of state (EoS) over the entire density range, such that various thermodynamic properties can be calculated with the EoS. While majority of EoS’s published are for the stable fluid region only, few attempted the liquid-hexact transition region. All the EoS’s currently available are incapable of quantitative descriptions of the phase transitions. Here we construct a simple EoS to reproduce high-precision simulation data for all the stable liquid, liquid-hexatic transition region and hexatic phase. A global EoS is then obtained when the new EoS is smoothly united with a revisited EoS for the solid phase. Using this global equation, we are able to accurately identify all the phases and the phase transitions from the stable liquid to hexatic, then to solid phases.