Finite Size Research Articles

Impact of ageing on structure of random sequentialadsorption packings of discorectangles

Abstract The ageing processes in the systems of elongated particles (discorectangles) adsorbed on a plane was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was tested. The initial jammed state was produced using the random sequential adsorption (RSA) model. The transition from the jammed to equilibrium states were 
performed via translational and rotational Brownian motions. An aspect ratio of the particles (length-to-width ratio) was varied within the range $\varepsilon=1-12$. At $\varepsilon < 10$ the relaxation into the isotropic state %with $S=0$ 
was always observed. In the intermediate range, $10 \le \varepsilon \le 11$, the relaxation transition into the states with ordered domains was observed. Particularly, for $ \varepsilon=10$ this transition was related with significant finite size scaling effects. For particles with $\varepsilon=12$ formation of the large scale quasi-nematic domains and unlimited domain growth was observed. The impact of the relaxation on the domain structure, porosity, percolation connectivity and tracer particle diffusion in such barrier systems was also discussed.

Subvolume method for SU(2) Yang-Mills theory at finite temperature: topological charge distributions

We apply the previously-developed sub-volume method to study the θ-dependence of the four-dimensional SU(2) Yang-Mills theory at finite temperature. We calculate the first two coefficients, the topological susceptibility χ and the fourth cumulant b2, in the θ-expansion of the free energy density around the critical temperature (Tc) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes 243, 323, 483 to monitor finite size effects, while the temporal size is fixed to be 8. The systematic uncertainty associated with the sub-volume extrapolation is studied with special care. The sub-volume method allows us to determine the values of b2 much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of b2 around Tc. Our numerical results suggest that the θ-dependence of the free energy density near θ = 0 changes from 4χ(1 − cos(θ/2)) to χ(1 − cos θ) as the temperature crosses Tc.

Investigation of the dynamics of interaction of a cluster of primordial black holes with stellar cluster

In this paper, we revise dynamical constraint on primordial black hole (PBH) abundance following the effect of their interaction with stellar cluster in dwarf galaxy Eridanus II in case of PBH clustering. We consider scattering of stars on PBH cluster as a whole, dynamical friction of stars inside cluster and finally we are taking into account tidal forces’ effects due to the finite size of PBH cluster. We obtain the rate of change of kinetic energy of the stars and PBHs to make conclusion about constraints on clusters.

Local Permeability of a Metasurface in the MHz and GHz Ranges

The work is dedicated to the study of the magnetic response of a metasurface made of split ring resonators (meta-atoms) in the MHz and GHz ranges. A new method for calculating the local permeability of a metasurface in the MHz frequency range is proposed, taking into account the finite sizes of the elements, and for the first time, a result of high degree of accuracy matching with experimental values has been obtained. In the GHz range, additional factors such as the retardation effect, non-uniform current distribution in the meta-atom, and the complexity of the nature of meta-atoms’ interaction compared to the MHz range are also considered, in particular, the emergence of electrical interaction between them.

Effects of nonlinearity on Anderson localization of surface gravity waves

Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves is a long-standing debate. Here, we show that the nonlinearity strengthens the localization of surface-gravity waves propagating in a canal with a random bottom. We also show experimentally how the localization length depends on the nonlinearity, which has never been reported previously with any type of wave. To do so, we use a full space-and-time-resolved wavefield measurement as well as numerical simulations. The effects of the disorder level and the system’s finite size on localization are also reported. We also highlight the first experimental evidence of the macroscopic analog of Bloch’s dispersion relation of linear hydrodynamic surface waves over periodic bathymetry.

Effects of nonlinearity on Anderson localization of surface gravity waves

Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves is a long-standing debate. Here, we show that the nonlinearity strengthens the localization of surface-gravity waves propagating in a canal with a random bottom. We also show experimentally how the localization length depends on the nonlinearity, which has never been reported previously with any type of wave. To do so, we use a full space-and-time-resolved wavefield measurement as well as numerical simulations. The effects of the disorder level and the system’s finite size on localization are also reported. We also highlight the first experimental evidence of the macroscopic analog of Bloch’s dispersion relation of linear hydrodynamic surface waves over periodic bathymetry.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems

Abstract We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates.

 Such reaction coordinates prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the reaction coordinates. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Economical routes to size-specific assembly of self-closing structures.

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity.

Estimation of the Largest Lyapunov Exponent for a Model of Cross-Shaped Waves in a Rectangular Channel of Finite Size

Estimation of the Largest Lyapunov Exponent for a Model of Cross-Shaped Waves in a Rectangular Channel of Finite Size

Long-time properties of generic Floquet systems are approximately periodic with the driving period

A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.

A correction algorithm of geometric unsharpness for neutron radiographs via adaptive fusion and total variation

The mobility of accelerator-based neutron sources has laid the foundation for the miniaturization of neutron radiography facilities in response to the increasing industrial requirements. Compared to traditional reactors and spallation neutron sources, miniaturized neutron radiography facilities based on accelerator neutron sources face challenges in achieving a sufficiently high collimation ratio. It leads to a pronounced level of geometric unsharpness on neutron radiographs, which arises from a finite source size and beam divergence. The presence of blurriness in radiographs significantly impairs the ability to accurately visualize the internal structures of the test objects, thus hindering observation. An algorithm combining adaptive fusion with total variation was proposed to correct the geometric unsharpness for neutron radiographs in this paper. In contrast to most traditional restoration algorithms that relied on regularization terms or filters, our proposed method offered both initial restoration and further restoration. The initial restoration procedure involved the utilization of the Richardson-Lucy algorithm coupled with the l0 smoothing method. This adaptive fusion technique was employed to enhance the sharpness of edges and denoise the neutron radiographs. Finally, the result of the adaptive fusion was embedded into a deblurring model based on total variation to further preserve the edges and restore more details during further restoration. In the experiments, it was demonstrated that our correction algorithm effectively preserved the prominent edges and the details in both the simulated and real neutron radiographs of thin and thick objects, exhibiting fewer ringing effects than traditional algorithms. It is worth mentioning that our work is primarily applicable and significant to neutron generators, but not for reactors or spallation neutron sources that can deliver much better images.

A soluble model for synchronized rhythmic activity in ant colonies

Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise.

Fluid simulations for a finite size plasma

Studies on finite-size plasma have attracted a lot of attention lately. They can form by ionizing liquid droplets by lasers. The dynamical behavior of such plasma droplets is, therefore, a topic of significant interest. In particular, questions related to the linear and nonlinear characteristics (associated with the inhomogeneous density typically at the edge of the droplet), the behavior of plasma expansion, etc., are of interest. A one-dimensional fluid simulation study has been carried out to investigate this behavior. It is observed that a slight imbalance in the charge density leads to oscillations that are concentrated and keep acquiring higher amplitude and sharper profiles at the inhomogeneous edge region. Such oscillations lead to the expansion of the droplet. Though the fluid description breaks when the sharpness of these structures becomes comparable to the grid size, it provides a reasonable estimate of wave-breaking time. The presence of dissipative effects such as diffusion is shown to arrest the sharpness of these structures. The dynamics of these structures in the presence of an externally applied oscillating electric field corresponding to long wavelength radiation have also been studied.

Modeling drag coefficients of spheroidal particles in rarefied flow conditions

Transport of particles in flows is often modeled in a combined Eulerian–Lagrangian framework. The flow is evaluated on an Eulerian grid, while particles are modeled as Lagrangian points whose positions and velocities are evolved in time, resulting in particle trajectories embedded in the time-dependent flow field. The method essentially resolves the flow field in complex geometries in detail but uses a closure model for the particle dynamics aimed at including the essential particle–fluid interactions at the cost of detailed small-scale physics. Rarefaction effects are usually included through the phenomenological Cunningham correction on the drag force experienced by the particles. In this Lagrangian point-particle approach, any explicit reference to the finite size and the shape of the particles, and their local orientation in the flow field, is typically ignored. In this work we aim to address this gap by deriving, from fully-resolved Direct Simulation Monte Carlo (DSMC) studies, heuristic or closure models for the drag force acting on prolate and oblate spheroidal particles with different aspect ratios, and a fixed orientation, in uniform ambient rarefied flows covering the transition regime between the continuum and free-molecular limits. These closure models predict the drag in the transition regime for all considered parameter settings (validated with DSMC data). The continuum limit is enforced a priori and we retrieve the free-molecular limit with reasonable accuracy (based on comparisons with literature data). We also include in the models the capability to predict effects related to basic gas-surface interactions via the tangential momentum accommodation coefficient. We furthermore assess the validity of the proposed closure model for particle dynamics in proximity to solid walls. This investigation extends our previous work, which focused on small aspect ratio spheroids with exclusively diffusive gas-surface interactions [see Livi et al. (2022)]. The derived models are obtained for isothermal, subsonic flows relevant for particle contamination control in semiconductor manufacturing.

Fluid simulations for a finite size plasma

Fluid simulations for a finite size plasma

Contrasting Views of the Electric Double Layer in Electrochemical CO2 Reduction: Continuum Models vs Molecular Dynamics.

In the field of electrochemical CO2 reduction, both continuum models and molecular dynamics (MD) models have been used to understand the electric double layer (EDL). MD often focuses on the region within a few nm of the electrode, while continuum models can span up to the device level (cm). Still, both methods model the EDL, and for a cohesive picture of the CO2 electrolysis system, the two methods should agree in the regions where they overlap length scales. To this end, we make a direct comparison between state-of-the-art continuum models and classical MD simulations under the conditions of CO2 reduction on a Ag electrode. For continuum modeling, this includes the Poisson-Nernst-Planck formulation with steric (finite ion size) effects, and in MD the electrode is modeled with the constant potential method. The comparison yields numerous differences between the two modeling methods. MD shows cations forming two adsorbed layers, including a fully hydrated outer layer and a partial hydration layer closer to the electrode surface. The strength of the inner adsorbed layer increases with cation size (Li+ < Na+ < K+ < Cs+) and with more negative applied potentials. Continuum models that include steric effects predict CO2 to be mostly excluded within 1 nm of the cathode due to tightly packed cations, yet we find little evidence to support these predictions from the MD results. In fact, MD shows that the concentration of CO2 increases within a few Å of the cathode surface due to interactions with the Ag electrode, a factor not included in continuum models. The EDL capacitance is computed from the MD results, showing values in the range of 7-9 μF cm-2, irrespective of the electrolyte concentration, cation identity, or applied potential. The direct comparison between the two modeling methods is meant to show the areas of agreement and disagreement between the two views of the EDL, so as to improve and better align these models.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

Distribution-Free Prediction Intervals Under Covariate Shift, With an Application to Causal Inference

Owing to its appealing distribution-free feature, conformal inference has become a popular tool for constructing prediction intervals with a desired coverage rate. In scenarios involving covariate shift, where the shift function needs to be estimated from data, many existing methods resort to data-splitting techniques. However, these approaches often lead to wider intervals and less reliable coverage rates, especially when dealing with finite sample sizes. To address these challenges, we propose methods based on a pivotal quantity derived under a parametric working model and employ a resampling-based framework to approximate its distribution. The resampling-based approach can produce prediction intervals with a desired coverage rate without splitting the data and can be easily applied to causal inference settings where a shift in the covariate distribution can occur between treatment and control arms. Additionally, the proposed approaches enjoy a double robustness property and are adaptable to different prediction tasks. Our extensive numerical experiments demonstrate that, compared to existing methods, the proposed novel approaches can produce substantially shorter conformal prediction intervals with lower variability in the interval lengths while maintaining promising coverage rates and advantages in versatile usage. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.