Limit Of Large Size Research Articles

Exact results on the dynamics of the stochastic Floquet-East model

Abstract We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size, this model has a large deviation phase transition between active and inactive dynamical phases. We also compute the finite time and size scaling of general space-time fluctuations, which for the case of inactive regions gives rise to dynamical hydrophobicity. We also discuss how, through the Trotter limit, these exact results also hold for the continuous-time East model, thus proving long-standing observations in kinetically constrained models. Our results here illustrate the applicability of exact tensor network methods for solving problems in many-body stochastic systems.

Using gas-assisted electrospinning to design rod-shaped particles from starch for thickening agents and Pickering emulsifiers

Starch's large particle size and compact semi-crystalline structure limit its effectiveness as an emulsifier and shear-reversible thickener. To address this, we used gas-assisted electrospinning to convert large starch granules into thin fibers and then into rod-shaped particles for use as starch-based thickeners and emulsifiers. Manipulating the starch concentration in formic acid, and the electrospinning parameters, caused the jetted polymers to form different shapes. At low starch content (<5 w/w%), electrospraying produced smaller particles (0.4–3.0 μm diameter). At higher concentrations, the polymers tangled and favored the formation of fibers (0.5–3.9 μm diameter). The starch's morphological behavior was fine-tuned by adjusting flow rate, coaxial airflow pressure, voltage, needle gauge, and jetting distance. Extensive formic acid treatment (> 4 days) caused a fiber-to-bead transition. Fiber suspensions exhibited ~106-times higher viscosity (3215 Pa·s at a shear rate of 0.002 s−1) than unmodified starch. High-shear and ultrasonication were used post-spin to chop the fibers into rod-shaped particles (4, 6 and 8 μm length), which were used as effective emulsifiers. The longest rods (8 μm) stabilized emulsions with the smallest droplets (12 μm). Using food-safe polymers, this study demonstrated that the shape of particles plays important roles in modulating the material functionalities.

Triple junction excess energy in polycrystalline metals

The energetics of triple lines are often negligible in polycrystalline systems, but may play a significant role in the finest nanocrystals, and in fact lower the excess defect energies of those polycrystals. This paper develops a methodology to assess polycrystalline average grain boundary and triple junction excess energies for pure fcc metals Ni, Cu, Al, Pd, Pt, Ag and Au using embedded atom method potentials. It is found that there are correlations between the triple line energy and physical quantities such as grain boundary and dislocation line energy, but with a negative sign indicating that triple junctions reduce intergranular excess energy per area on average. The relationship with grain boundary energy is of order ∼−4.5 × 10−10 m, and the triple junction energy is about −1/12 of the dislocation line energy. Despite their low energy, triple junctions can significantly affect total system energy due to their high density in the finest nanocrystals; for example, 6-nm Pd nanocrystals have an effective intergranular energy of ∼0.83 J/m2 (compared with the large grain size limit of 0.93 J/m2), translating to a measurable bulk excess enthalpy of ∼6 kJ/mol. Such excess enthalpy is experimentally assessable, and the present framework can be used to measure triple junction energies. For instance, re-analyzing data of Lu and Sun (Phil. Mag., 1997) we obtain grain boundary and triple junction energies of 0.33 J/m2 and −3.0 × 10−10 J/m respectively for Selenium nanocrystals, which can be compared with modeled values of 0.76 J/m2 and −1.02 × 10−10 J/m by using our method with a published bond-order potential for Se.

Level statistics of the one-dimensional dimerized Hubbard model

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

Averages of products of characteristic polynomials and the law of real eigenvalues for the real Ginibre ensemble

We review an elementary derivation of the Borodin–Sinclair–Forrester–Nagao Pfaffian point process, which characterizes the law of real eigenvalues for the real Ginibre ensemble in the large matrix size limit, in terms of averages of products of characteristic polynomials. This derivation relies on a number of interesting structures associated with the real Ginibre ensemble such as the hidden symplectic symmetry of the statistics of real eigenvalues. It leads to a representation for the [Formula: see text]-point correlation function for any [Formula: see text] in terms of an integral over the symmetric space [Formula: see text] and this paper gives the proof of asymptotic exactness for this integral.

Finite-size scaling in kinetics of phase separation in certain models of aligning active particles.

To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.

Convergence of ensemble forecast distributions in weak and strong forcing convective weather regimes

AbstractThe constraint of computational power and the huge number of degrees of freedom of the atmosphere means a sampling uncertainty exists in probabilistic ensemble forecasts. In our previous study, the uncertainty could be quantified, creating a convergence measure which converges proportional to in the limit of large ensemble size . This power law can then be extrapolated to determine how sampling uncertainty would decrease with larger ensemble sizes and hence find the necessary ensemble size. It is unknown, however, how the sampling uncertainty depends on different weather regimes. This study extends the previous idealised ensemble developed, by including weak and strong forcing convective weather regimes, to look at how sampling uncertainty convergence differs in each. Two ‐member ensembles were run, with weak and strong forcing respectively. Comparisons with a kilometre‐scale weather prediction model ensured realistic weak and strong forcing regimes by comparing the rain, convective available potential energy (CAPE), convective adjustment timescale, and distribution shapes throughout the diurnal cycle. Differences in distribution shape between the regimes led to differences in the convergence measure. Large differences in spread between weak and strong forcing runs throughout the hr period led to large differences in sampling uncertainty of the mean and standard deviation, which could be quantified according to well‐known equations. The timing of these differences was case‐dependent. For extreme statistics such as the quantile and for cases where there was precipitation, the moisture variables for the weak forcing case had the largest sampling uncertainty and required the most members for convergence proportional to . This was due to the tails of the weak forcing moisture variables containing the least amount of density. Different ensemble sizes will hence be required depending on whether one is in the weak or strong forcing convective weather regime.

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

Breakdown of a concavity property of mutual information for non-Gaussian channels

Abstract Let $S$ and $\tilde S$ be two independent and identically distributed random variables, which we interpret as the signal, and let $P_{1}$ and $P_{2}$ be two communication channels. We can choose between two measurement scenarios: either we observe $S$ through $P_{1}$ and $P_{2}$, and also $\tilde S$ through $P_{1}$ and $P_{2}$; or we observe $S$ twice through $P_{1}$, and $\tilde{S}$ twice through $P_{2}$. In which of these two scenarios do we obtain the most information on the signal $(S, \tilde S)$? While the first scenario always yields more information when $P_{1}$ and $P_{2}$ are additive Gaussian channels, we give examples showing that this property does not extend to arbitrary channels. As a consequence of this result, we show that the continuous-time mutual information arising in the setting of community detection on sparse stochastic block models is not concave, even in the limit of large system size. This stands in contrast to the case of models with diverging average degree, and brings additional challenges to the analysis of the asymptotic behavior of this quantity.

Diffusive persistence on disordered lattices and random networks.

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or, in general, that the node remained active or inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P(t,L)∼t^{-θ} with an exponent θ≃0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ≃0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power law P(t,L)∼L^{-zθ} with z≃2.86 instead of the value of z=2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdős-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions.

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

YOLO sparse training and model pruning for street view house numbers recognition

This paper proposes a YOLO (You Only Look Once) sparse training and model pruning technique for recognizing house numbers in street view images. YOLO is a popular object detection algorithm that has achieved state-of-the-art performance in various computer vision tasks. However, its large model size and computational complexity limit its deployment on resource-constrained devices such as smartphones and embedded systems. To address this issue, we use a sparse training technique that trains YOLO with L1 norm regularization to encourage the network to learn sparse representations. This results in a significant reduction in the number of parameters and computation without sacrificing accuracy. Furthermore, we apply a model pruning technique to the sparse-trained model to reduce the model size and computation. We evaluate our proposed method on the SVHN (Street View House Numbers) dataset. We show that it performs comparably to the original YOLO model while reducing the model size by 5% and the computation time by 7%. Overall, our proposed YOLO sparse training and model pruning technique provides an effective solution for deploying YOLO-based object detection models on resource-constrained devices.

Dynamics of information networks

AbstractWe explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (i, j) are randomly chosen to interact, with an edge drawn from i to j (and any other out-edge from i deleted) if j is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed.

The shirker’s dilemma and the prospect of cooperation in large groups

Cooperation usually becomes harder to sustain as groups become larger because incentives to shirk increase with the number of potential contributors to collective action. But is this always the case? Here we study a binary-action cooperative dilemma where a public good is provided as long as not more than a given number of players shirk from a costly cooperative task. We find that at the stable polymorphic equilibrium, which exists when the cost of cooperation is low enough, the probability of cooperating increases with group size and reaches a limit of one when the group size tends to infinity. Nevertheless, increasing the group size may increase or decrease the probability that the public good is provided at such an equilibrium, depending on the cost value. We also prove that the expected payoff to individuals at the stable polymorphic equilibrium (i.e., their fitness) decreases with group size. For low enough costs of cooperation, both the probability of provision of the public good and the expected payoff converge to positive values in the limit of large group sizes. However, we also find that the basin of attraction of the stable polymorphic equilibrium is a decreasing function of group size and shrinks to zero in the limit of very large groups. Overall, we demonstrate non-trivial comparative statics with respect to group size in an otherwise simple collective action problem.

Asymptotically matched extrapolation of fishnet failure probability to continuum scale

Motivated by the extraordinary strength of nacre, which exceeds the strength of its fragile constituents by an order of magnitude, the fishnet statistics became in 2017 the only analytically solvable probabilistic model of structural strength other than the weakest-link and fiber-bundle models. These two models lead, respectively, to the Weibull and Gaussian (or normal) distributions at the large-size limit, which are hardly distinguishable in the central range of failure probability. But they differ enormously at the failure probability level of 10−6, considered as the maximum tolerable for engineering structures. Under the assumption that no more than three fishnet links fail prior to the peak load, the preceding studies led to exact solutions intermediate between Weibull and Gaussian distributions. Here massive Monte Carlo simulations are used to show that these exact solutions do not apply for fishnets with more than about 500 links.The simulations show that, as the number of links becomes larger, the likelihood of having more than three failed links up to the peak load is no longer negligible and becomes large for fishnets with many thousands of links. A differential equation is derived for the probability distribution of not-too-large fishnets, characterized by the size effect, the mean and the coefficient of variation.Although the large-size asymptotic distribution is beyond the reach of the Monte Carlo simulations, it can by illuminated by approximating the large-scale fishnet as a continuum with a crack or a circular hole. For the former, instability is proven via complex variables, and for the latter via a known elasticity solution for a hole in a continuum under antiplane shear. The fact that rows or enclaves of link failures acting as cracks or holes can form in the large-scale continuum at many random locations necessarily leads to the Weibull distribution of the large fishnet, given that these cracks or holes become unstable as soon they reach a certain critical size. The Weibull modulus of this continuum is estimated to be more than triple that of the central range of small fishnets. The new model is expected to allow spin-offs for printed materials with octet architecture maximizing the strength–weight ratio.

Design and Validation of a Nonparasitic 2R1T Parallel Hand-Held Prostate Biopsy Robot With Remote Center of Motion

AbstractAn increasing number of grounded robots are being used in prostate interventions to improve clinical outcomes, but their large size and high-cost limit their popularity. Thus, we present a hand-held 3-degree-of-freedom (DoF) parallel robot with remote center of motion (RCM) for minimally invasive prostate biopsy applications, combining the flexibility of hand-held devices with the precision of robotic assistance. First, the kinematic structure of robotic assistance is introduced according to its design requirements. Then, the kinematic analysis of robotic assistance is carried out by using a simplified kinematic model. The kinematic parameters are designed according to the desired workspace. A prototype has been developed and validated in animal experiments. Twenty beagles of different sizes were selected for the robot-assisted and controlled experiments, resulting in target errors of 3.30 ± 1.63 mm and 5.40 ± 1.76 mm, respectively. The error of robot-assisted experiments was significantly better than in controlled experiments. Preliminary animal tests have demonstrated that the hand-held robot can improve the accuracy of free-hand biopsy punctures.

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold.

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

Finite Reservoirs Corrections to Hamiltonian Systems Statistics and Time Symmetry Breaking

We consider several Hamiltonian systems perturbed by external agents that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs and from the onset of processes breaking the time-reversal symmetry. We analyze exactly solvable oscillator systems and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics that are used to obtain numerous results.

Spontaneous symmetry breaking without ground state degeneracy in generalized N -state clock model

Spontaneous symmetry breaking is ubiquitous phenomenon in nature. One of the defining features of symmetry broken phases is that the large system size limit and the vanishing external field limit do not commute. In this work, we study a family of extensions of the $N$-state clock model. We find that the exact symmetry and the ground state degeneracy under the periodic boundary condition heavily depend on the system size, although the model has the manifest translation symmetry. In particular, the ground state can be unique and all excitations are gapped even when the phase exhibits non-commutativity of the two limits. Our model hence poses a question on the standard understanding of spontaneous symmetry breaking.

Divergent Stiffness of One-Dimensional Growing Interfaces.

When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness.