Effect Of System Size Research Articles

The effect of particle size distribution on the collapse of wet polydisperse granular materials

Low-saturation liquid-containing granular materials are commonly encountered in both natural and industrial settings, where interstitial liquids significantly affect the motion of particles, while particle size polydispersity plays a crucial role in determining the level of system cohesion. In this study, the collapse of wet polydisperse granular columns is numerically investigated based on the developed discrete element model, with corresponding dam-break experiments performed to validate our numerical model and methodology. The dependence of the dynamics and flow mobility on particle size distribution is primarily examined, and the underlying mechanisms are also explored by analyzing particle path lengths and average fidelity. Building upon the effective Bond number proposed using the mixing theory, a macroscopic cohesion parameter at the material scale is defined by considering the dependence of the collapse on the system size effect. The relevance of this cohesion parameter in describing different wet polydisperse granular collapses is further validated based on our designed experimental tests and DEM simulations. The approach of constructing the cohesion parameters at different scales can be extended to characterize cohesion effects in more complex wet polydisperse granular flows and describe their associated rheological behaviors.

System size effects on the free energy landscapes from molecular dynamics of phase-separating bilayers.

The "lipid raft" hypothesis proposes that cell membranes contain distinct domains of varying lipid compositions, where "rafts" of ordered lipids and cholesterol coexist with disordered lipid regions. Experimental and theoretical phase diagrams of model membranes have revealed multiple coexisting phases. Molecular dynamics (MD) simulations can also capture spontaneous phase separation of bilayers. However, these methods merely determine the signof the free energy change upon phase separation-whether or not it is favorable-but not the amplitude. Recently, we developed a workflow to compute the free energy of phase separation from MD simulations using the weighted ensemble method. However, while theoretical treatments generally focus on infinite systems and experimental measurements on mesoscopic to macroscopic systems, MD simulations are comparatively small. Therefore, if we are to put the results of these calculations into the appropriate context, we need to understand the effects the finite size of the simulation has on the computed free energy landscapes. In this study, we investigate this phenomenon by computing free energy profiles for a model phase-separating system as a function of system size, ranging from 324 to 10 110 lipids. The results suggest that, within the limits of statistical uncertainty, bulk-like behavior emerges once the systems contain roughly 4000 lipids.

Flow patterns and energy spectra in forced quasi-two-dimensional turbulence: effect of system size and damping rate

An experimental investigation is conducted to study the flow patterns, spectral properties and energy fluxes in thin-layer turbulence with varying system sizes and damping rates. It is found that although a system-size vortex (an indicator of spectral condensation) occurs for small system sizes and does not for large ones, the spectra for different system sizes consistently exhibit a scaling close to $k^{-3}$ in inverse cascade (another indicator of spectral condensation). On the other hand, under a fixed system size larger than the friction-dominated length scale, the energy spectrum in the inverse cascade range changes from $k^{-3}$ to $k^{-5/3}$ as the damping rate increases, suggesting that the friction-dominated length scale may not be a suitable parameter for predicting spectral transition. At lower damping rates and large system sizes, turbulent structures grow larger via inverse cascade, manifesting as long streamers, and the small-scale vortices are suppressed. This suppression leads to a reduction of energy flux at intermediate scales and a change in the spectral shape. The dimensionless Taylor microscale is found to exhibit a monotonic dependence on the damping rate. With the reduction in the damping rate, the Taylor microscale increases to become comparable with the forcing scale, and the spectrum in inverse cascade transits to a steeper scaling, $k^{-3}$ , indicating that the dimensionless Taylor microscale may be used as a diagnostic parameter for spectral transition.

Collective motion of binary chiral particle mixtures with environmental complex noise.

The strategies for demixing and sorting mixed-chirality particles are crucial in the biochemical and pharmaceutical industries. However, whether chiral mixed particles can effectively separate in more complex spatial environments remains unresolved. In this paper, we explore the collective motion of binary chiral particle mixtures with environmental complex noise in the binary chiral Vicsek model (BCVM). We discover that the noisy region ratio, λ, significantly influences the separation behavior and spatial distribution of binary mixtures, unveiling system states not observed in uniform environments. Additionally, varying the chirality of particles reveals four distinct phases in our model. In the Vicsek bands phase (small chirality), an increase in λ can, under certain conditions, promote segregation rather than consistently hindering the demixing process. Conversely, for large chirality, localized dynamics and a homogeneous phase emerge, reducing the impact of λ on separation behavior. Notably, when chirality and activity are comparable, macrodrops and microflock phases appear, with a mixed-segregated state transition occurring at a critical λ_{c}. For λ<λ_{c}, chiral separation occurs with particles confined to the noise-free region. However, when λ>λ_{c}, particles gradually migrate to the noisy region, disrupting the separation. Further, we discuss the effects of multiple factors, including chirality, velocity, noise magnitude, particle number, and system size on λ_{c}. We also identify an optimal interaction radius at which λ_{c} reaches its peak value. Our findings may inspire strategies for achieving spontaneous demixing and spatial migration of mixed-chirality particles in complex environments.

Relaxation dynamics in the self-propelled Voronoi model for epithelial monolayers

Cell monolayers and epithelial tissues display slow relaxation dynamics during the reversible transition between mesenchymal and epithelial cells, a phenomenon directly relevant to embryogenesis, tumor metastases, and wound healing. In active cells, persistent motion induces collective dynamics that significantly influence relaxation behavior. To better understand the role of persistence in cell relaxations, we perform extensive simulations and employ cage-relative measures to address the previously overlooked system size effects in model active cells. We identify the glass transition at various persistence values, demonstrating conventional near-equilibrium supercooled dynamics at low persistence. However, highly persistent cells exhibit distinctive intermittent dynamics associated with intermittent local T1 transitions, where cell velocity correlates over space with a characteristic length ξ. More significantly, we formulate a universal relationship predicting the global relaxation time based on the T1 transition and the spatial velocity correlation across a wide range of persistence values. Specifically, the relaxation time demonstrates a power-law dependence on the irreversible T1 transition rate, multiplied by exp(ξ). Here, ξ vanishes at small persistence in nearly equilibrated cells, and the irreversible T1 transition rate diminishes towards the mode-coupling glass transition point. Published by the American Physical Society 2024

A model for the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution

Nanocrystalline materials are a popular metamaterial used to control heat transport in semiconductor industrial applications. An accurate and reliable theoretical model is urgently needed but challenging for elucidating detailed microscopic heat transfer phenomena. In this study, we develop a mathematical model to predict the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution. The model first obtains the effective scattering rate of grain boundaries in single-grain-size materials, and then integrates the Landauer’s system transmission concept and series transmission concept to become applicable to multiple grain sizes. It takes into account not only intrinsic and grain boundary scattering effects, but also the effects of finite system size and grain size distribution. Numerical samples of silicon nanocrystals with single grain size, dual size, constant grain size distribution, and logarithmic normal grain size distribution are constructed and full-spectrum Monte Carlo simulations are performed for comparison. The excellent agreement observed between model predictions and simulation results validates the accuracy of the proposed theoretical model. This model will be very helpful in designing micron-scale thermal manipulation systems using nanostructures.

A study of layered holographic superconductor

We have investigated a holographic model of a multi-layered superconductor in (2+1)-dimensions using the AdS/CFT correspondence. This correspondence allows us to study strongly interacting condensed matter systems through a weakly interacting gravitational theory. Our study focused on the effects of a finite system size on the superconductor’s properties. We observed significant variations in the critical temperature and critical magnetic field depending on the number of layers and the spacing between them. Notably, our results capture the transition from a two-dimensional (2D) to a three-dimensional (3D) behavior in the limit of a large number of closely spaced layers. This transition signifies a change in how the superconductivity operates within real material.

Parametric Decay of a Kinked Alfvén Wave Packet: 3D Magnetohydrodynamic Simulations

Large amplitude Alfvénic fluctuations, sometimes leading to localized inversions of the magnetic field, called switchbacks, are a common but poorly understood phenomenon in the solar wind. In particular, their origin(s), evolution, and stability within solar wind conditions are yet to be fully understood. Simulations modeling switchbacks have previously studied their stability in 2D. Here, we investigate the decay process of Alfvén wave packets via MHD simulations in 3D by characterizing the effects of system size, aspect ratio, and propagation angle on the decay rate. We show that the initial wave packet is unstable to parametric instabilities that develop compressible and Alfvénic secondary modes in the plane of, and transverse to, the initial wave packet propagation direction. The growth of transverse modes, absent in 2D simulations, increases the decay rate of the wave packet. We finally discuss the implications of our results for lifetime estimates of switchbacks and wave energy conversion in the solar wind.

Simulating Brownian motion in thermally fluctuating viscoelastic fluids by using the smoothed profile method

To investigate the Brownian motion of individual particles suspended in viscoelastic fluids, the stochastic smoothed profile method (SPm) for direct numerical simulation is developed by extending deterministic SPm for suspensions in viscoelastic media. To simulate viscoelastic flow driven by thermal fluctuations in the suspending medium, the random stress in the fluid momentum equation as well as the random driving force for the conformation tensor in the Oldroyd-B model are incorporated according to the fluctuating hydrodynamics and fluctuating viscoelasticity formalisms. The thermal equilibrium and dynamical properties calculated by using numerical simulations successfully reproduce the analytic predictions, validating the direct simulation for the coupled fluctuating Navier–Stokes and Oldroyd-B equations and for the coupling between the stochastic viscoelastic medium and individual particles. As an application of the stochastic SPm, we investigate finite system-size effects under periodic boundary conditions (PBCs) on the passive microrheological relationship between the mean-square displacement (MSD) of a Brownian particle and the medium's dynamic modulus. Comparing the modulus that was microrheologically calculated from the MSD with the input modulus reveals that the effect of periodic image cell interaction appears not only in the long-time diffusive regime but also in the short-time region. A frequency-dependent finite system-size correction is implemented by phenomenologically extending the long-time diffusive regime correction, allowing passive microrheology analysis under PBCs. This result can be directly applied to other mesoscale numerical simulations including coarse-grained molecular dynamics and dissipative particle dynamics simulations.

Turbulent spot formation in three-dimensional yukawa liquids using large-scale molecular dynamics simulation—effect of system size

We have performed classical ‘first principles’ 3D Molecular Dynamics (MD) simulation of plane-Couette flow (PCF) in a 3D Yukawa liquid. The main aim of the present investigation is to study the effect of stream-wise (flow-direction) and span-wise (transverse direction to the flow) width on the subcritical transition to turbulence in plane Couette flow (PCF), separately. In the past, taking very large-aspect ratio systems, subcritical transition to turbulence in PCF has been studied in great detail. However, the effect of stream-wise and span-wise width on the turbulent dynamics separately, have not been studied in detail. In the present work, we have investigated the effect of stream-wise and span-wise width or length and found that the stream-wise length enhances the large-scale energy, which gives rise to strong large-scale flow, and span-wise width enhances the small-scale energy, which gives rise to strong small-scale structures. In other words, topology of the turbulent spot is observed to change with the change in system size. The spectral separation between the modes governing the large and small-scale dynamics improves with the increase in system sizes. The connection between the stream-wise vortices and the stream-wise velocity streaks is investigated in details. We have found that the number stream-wise velocity streaks is one unit larger than the number of stream-wise vortices. A qualitative comparison between the results obtained from the MD simulation and the hydrodynamics experiment is presented in this article. The behavior of the system was observed to vary with the range of interactions among the dust grains.

Molecular dynamics simulation of shock waves in Fe and Fe–C: Influence of system characteristics

Pressure-induced phase transformation in iron and its alloys is a classic research topic in solid-state physics, material science, and geophysics. The crystal structure of iron undergoes a phase transformation at a hydrostatic pressure of 13 GPa, changing from a body-centered cubic system to a hexagonal close-packed system. Although extensive research has been carried out on the transformation in iron by using molecular dynamics simulations, there is very limited literature that focuses on the contribution of parent phase orientations, system size, and impurities to the phase evolution. In this work, classic molecular dynamics simulations have been employed to investigate the effects of system size, lattice orientation, and impurity concentration on the pressure-induced phase transformation of iron and iron alloys for the first time. Our results show that the lattice orientation has a strong influence on the phase transition behavior, while the influence of carbon is small. The phase transition is slightly delayed with increasing carbon content, whereas the transition pressure increases from [001] to [011] to [111] orientation. The amount of twinning and stacking faults highly depends on the orientation. It is easiest for solitary waves to travel through [111] lattice orientation. The addition of carbon has a slow-down effect on shock velocities, and this effect increases with carbon content and lattice orientation of the samples from [001] to [011] to [111].

Molecular dynamics study of thermal transport across diamond/cubic boron nitride interfaces

The thermal transport properties at the interface of diamond and cubic boron nitride (c-BN) heterostructures significantly influence heat dissipation in high-power electronic and optoelectronic devices. However, a fundamental understanding of the various parameters modulating the interfacial thermal conductance is still lacking. In this work, we employ non-equilibrium molecular dynamics (NEMD) simulations to systematically investigate the effects of system size, temperature, and defect density on the interfacial thermal conductance across diamond/c-BN interfaces. The results indicate a positive correlation between system length and interface thermal conductance when below the phonon mean free path threshold, attributable to ballistic phonon transport regimes in smaller domains. Additionally, we observe an incremental enhancement in interface thermal conductance with increasing temperature, stemmed from intensified phonon-phonon interactions and reduced boundary scattering of thermal energy carriers. The introduction of vacancy and twinning defects is found to hinder interfacial thermal transport due to heightened phonon scattering processes that impede phononic transmission. The interatomic interactions and lattice dynamics are analyzed to provide insights into the underlying thermal transport physics at the atomistic scale. By tuning the system length from 4 to 16 nm, temperature from 300 to 500 K, and defect density from 0 to 0.4%, we achieve tunable control of the interfacial thermal conductance. Our study elucidates the multiscale mechanisms governing thermal transport across diamond/c-BN and provides potential pathways to actively tailor interfacial thermal properties through structural and temperature engineering. The fundamental understandings are valuable for optimizing heat dissipation and enabling thermal management solutions in next-generation power electronics leveraging these materials.

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 106 and 4.5 × 109 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L−1. Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. We also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

Thermal transport of graphene-C3B superlattices and van der Waals heterostructures: a molecular dynamics study

Two-dimensional (2D) materials have attracted more and more attention due to their excellent properties. In this work, we systematically explore the heat transport properties of Graphene-C3B (GRA-C3B) superlattices and van der Waals (vdW) heterostructures using molecular dynamics method. The effects of interface types and heat flow directions on the in-plane interfacial thermal resistance (ITRip) are analyzed. Obvious thermal rectification is detected in the more energy stable interface, GRA zigzag-C3B zigzag (ZZ) interface, which also has the minimum value of ITRip. The dependence of the superlattices thermal conductivity (k) of the ZZ interface on the period length (l p ) is investigated. The results show that when the l p is 3.5 nm, the k reaches a minimum value of 35.52 W m−1 K−1, indicating a transition stage from coherent phonon transport to incoherent phonon transport. Afterwards, the effects of system size, temperature, coupling strength and vacancy defect on the out-of-plane interfacial thermal resistance (ITRop) are evaluated. With the increase of temperature, coupling strength and vacancy defect, ITRop are found to reduce effectively due to the enhanced Umklapp phonon scattering and increased probability of energy transfer. Phonon density of states and phonon participation ratio is evaluated to reveal phonon behavior during heat transport. This work is expected to provide essential guidance for the thermal management of nanoelectronics based on 2D monolayer GRA and C3B.

Nonlinear effect of grain elongation on the flow rate in silo discharge.

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda etal. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equationto predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

A comprehensive model of Drosophila epithelium reveals the role of embryo geometry and cell topology in mechanical responses.

In order to understand morphogenesis, it is necessary to know the material properties or forces shaping the living tissue. In spite of this need, very few in vivo measurements are currently available. Here, using the early Drosophila embryo as a model, we describe a novel cantilever-based technique which allows for the simultaneous quantification of applied force and tissue displacement in a living embryo. By analyzing data from a series of experiments in which embryonic epithelium is subjected to developmentally relevant perturbations, we conclude that the response to applied force is adiabatic and is dominated by elastic forces and geometric constraints, or system size effects. Crucially, computational modeling of the experimental data indicated that the apical surface of the epithelium must be softer than the basal surface, a result which we confirmed experimentally. Further, we used the combination of experimental data and comprehensive computational model to estimate the elastic modulus of the apical surface and set a lower bound on the elastic modulus of the basal surface. More generally, our investigations revealed important general features that we believe should be more widely addressed when quantitatively modeling tissue mechanics in any system. Specifically, different compartments of the same cell can have very different mechanical properties; when they do, they can contribute differently to different mechanical stimuli and cannot be merely averaged together. Additionally, tissue geometry can play a substantial role in mechanical response, and cannot be neglected.

NLO Scattering in ϕ 4 Theory Finite System Size Corrections Self-Consistency

Previously a 2 → 2 NLO scattering amplitude for massive ϕ 4 theory with periodic boundary conditions was derived to investigate finite system size effects. This utilized new techniques and results, and as such benefited from self-consistency checks. Here we revisit the self-consistency of the derived amplitude, in order to more rigorously establish the self-consistency. Special attention is given to potentially pathological sums, which sets up for numerical evaluation investigating the finite system effects on quantities of interest, such as the effective coupling.

Thermophoresis of nanoparticles in the transition regime

The thermophoresis of nanoparticles suspended in gas is investigated in the transition regime by molecular dynamics simulations. It is found that there exists significant discrepancy between the simulation results and the theoretical predictions for the thermophoretic force, which is attributed to the adsorption of gas molecules on nanoparticles and the gas–particle non-rigid body collisions. By using the effective particle radius, the simulation results and Talbot et al.'s equation could agree with each other in the transition regime. In addition, the effect of the finite system size of the molecular dynamics simulations is non-negligible, and the simulation results modified by effective particle radius can coincide with Phillips' equation quite well. Therefore, for particles of a few nanometers, the non-rigid body collision effect and the adsorption of gas molecules and the effective radius of the nanoparticle under strong gas–particle coupling should be taken into account in the theoretical model. The investigation presented in this paper provides guidance for the application of nanoparticles in aerosol science.

Small ponds have stronger potential for net nitrogen removal: Insight from direct dissolved N2 measurement

Growing demands for watershed nitrogen (N) removal have called attention to abundant small bodies of water such as ponds, which have long been heralded as efficient storage and processing systems. Although pond conservation, restoration, and creation have been widely implemented to mitigate N pollution, information is limited regarding the impact of size—that is, whether N removal potential and efficiency are dependent upon pond size. We investigated the dynamics of N removal rates in 56 ponds from a hilly watershed by studying their bimonthly N2 concentrations and fluxes. Our results showed that smaller ponds performed better in net N removal. This can be discerned from the areal N2 fluxes, which were the highest in small ponds (< 4, 000 m2). The corresponding N2 fluxes (4.73 ± 4.53 mmol N2 m−2 d−1) were 2 to 14 times greater than those observed in larger ponds. The N removal efficiency, a metric used to describe the portions of the substrates released as N2, was also significantly higher in the small ponds (∼8.7 %) than in the larger ponds (∼5.0 %). Further regression analysis showed that both areal N2 flux and N removal efficiency were negatively correlated with pond area. The underlying mechanisms behind the size effects of N removal could be attributed to small ponds having larger sediment contact area to water volume ratios. Thus, smaller ponds allow more opportunities for N to interact with bioactive sediments than larger ponds. Overall, our findings contribute to the understanding of the distal role of pond size in affecting N removal. This research also provides a strong rationale for considering the effects of system size when implementing management practices dedicated to maximizing N removal.

Atomistic determination of Peierls barriers of dislocation glide in nickel

The Peierls barrier measures the lattice resistance to dislocation glide in crystalline solids. We use the nudged elastic band (NEB) method to calculate the Peierls barriers for screw and edge dislocation glide in a face-centered cubic (FCC) metal of Ni. The minimum energy paths (MEPs) across single or sequential Peierls barriers are determined under shear loading. The NEB results show the decreasing Peierls barrier with increasing shear stress, giving the Peierls stress at which the Peierls barrier vanishes. The effects of boundary condition and system size on Peierls barriers are studied by comparing strain- and stress-controlled NEB results. Furthermore, the free-end NEB methods are applied to determine MEPs with improved computational efficiency. The NEB results are also used to evaluate the energetic driving force of dislocation glide, which is consistent with that determined from the Peach-Koehler force. The accuracy of the present NEB results based on an empirical interatomic potential is assessed by comparison with a machine-learning potential. This work demonstrates the robust and efficient quantification of Peierls barriers to dislocation glide in an FCC metal, and it lays a solid foundation for the atomistic determination of Peierls barriers in compositionally complex alloys with the FCC structure in future studies.