Ballistic Deposition Research Articles

Ballistic deposition with memory: A new universality class of surface growth with a new scaling law

Motivated by recent experimental studies in microbiology, we suggest modifying the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its neighbors. By studying the statistics of surfaces in this model, we obtain three independent critical exponents: the growth exponent β=5/4, the roughening exponent α=2, and the new (size) exponent γ=1/2. The model requires modifying the Family-Vicsek scaling, resulting in the dynamical exponent z=α+γβ=2. This modified scaling collapses the surface width vs time curves for various lattice sizes. This previously unobserved universality class of surface growth could describe the surface properties of a wide range of natural systems. Published by the American Physical Society 2024

A study of the competitive growth model due to random deposition mixed with a small fraction of ballistic deposition

A study of the competitive growth model due to random deposition mixed with a small fraction of ballistic deposition

Machine learning method for roughness prediction

This work aims to employ machine-learning models, specifically neural networks, to predict the time evolution of the global surface roughness in a lattice model that represents a film growing on a d-dimensional substrate. We analyze the well-known ballistic deposition (BD) model for d=1, 2 since it presents strong corrections to the scaling, making it difficult to observe directly, via effective scaling exponents, its correspondence with the Kardar-Parisi-Zhang (KPZ) universality class. As an alternative to overcome this difficulty, we first intend to learn the time evolution of the global roughness for substrate sizes that are computationally viable to simulate. To test the learning, we apply two different methodologies for d = 1: the first one learns the Family-Vicsek scaling relation, and by doing the reverse transformation, we get the global roughness as a function of the time, and the second one learns the kinetic roughening directly from the time series data. For growth in d = 2 where applications arise and no exact KPZ scaling exponents are known, we apply the second methodology. However, we employ a more resilient learning model tailored for time series problems. Hence, the time required to generate the same amount of data, showing the evolution of global roughness, is reduced dramatically. Importantly, machine learning techniques capture the scaling corrections of the BD model, predicting an effective global roughness exponent, α, calculated from the learned data extracted from very large lateral sizes and times that cannot be simulated using lattice models. Our prediction is consistent with accurate estimates of the KPZ roughness exponent reported in the literature for d = 2.

The “suevite” conundrum, Part 2: Re‐examining the type locality at the Ries impact structure, Germany

AbstractOne of the most common types of allochthonous impactite produced in hypervelocity impact events is impact breccia that contains melt particles. In numerous terrestrial hypervelocity impact structures such melt‐bearing breccias have been termed “suevite,” after the type locality at the Ries impact structure, Germany. Despite its widespread occurrence, the origin, emplacement, and classification of suevite remains debated. In this contribution, we re‐examine the nature and origin of suevite at the Ries impact structure. The results of new field and laboratory investigations, when combined and synthesized with results from previous studies, lead to a multi‐stage model for the origin and emplacement of allochthonous impactites during the Ries impact event. Following the creation of a transient cavity the so‐called Bunte Breccia and “megablocks” were emplaced via ballistic sedimentation and subsequent radial flow during the excavation stage to form a continuous ejecta blanket. At the end of the excavation stage, a mixture of melt and lithic fragments formed a lining to the transient cavity and it is this material that later became the crater, dike, and outer suevite (OS) units. The crater suevite represents the material from the displaced zone of the transient cavity that was transported and mixed but never left the cavity. The emplacement of dike suevite occurred during the modification stage as the crater suevite was intruded into fractures in the underlying crater floor. The OS and rare impact melt rocks overlying the ballistic (Bunte Breccia) ejecta deposits were emplaced as outwards‐directed ground‐hugging flows largely during the modification stage of crater formation. The OS flows varied both spatially and temporally in terms of the flow characteristics, from being dominated by solid particles and gas (cf. pyroclastic density currents) to a mixture of solid particles, liquid (impact melt), and minor gases (i.e., particulate impact melt‐rich flows). These particulate impact melt‐rich flows dominated by far. Minor “fallback” of material from an ejecta plume is evidenced by accretionary lapilli in the Nördlingen 1973 core. In summary, allochthonous impactites at the Ries impact structure are not unusual but are consistent with observations from other terrestrial and planetary craters, where melt‐rich impactites overly ballistic ejecta deposits both outside and inside crater rims and where melt‐rich impactites occur in crater interiors.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation (RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition (BD), etching, and restricted solid on solid (RSOS). The scaling exponents are obtained in both the (1 + 1)- and (2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1 – p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Geometrical exponents of contour loops on ballistic deposition model with power-law distributed noise

In this paper, we study geometrical properties of contour loops to characterize the morphology of the porous ballistic deposition model with power-law distributed noise. In this model, rod-like particles with variable lengths instead of homogeneous particles are deposited, the length of each rod, l, is determined by a power-law distribution, P(l)∼l−(μ+1), and μ indicates the power-law strength exponent. The accumulation of rods with different lengths leads to a porous structure. The porous structure is converted into contour loops by using the Hoshen–Kopelman algorithm and the complexity and fractal features of the loops are investigated. On the other hand, the distributions of loops indicating the porosity distribution of the growth rough surfaces are investigated. The fractal dimension of the contour set, d, the fractal dimension of each loop, Df, cumulative distributions exponent of areas, ξ, and the perimeter distribution exponent, τ, are calculated for the investigated porous structures. Our results show that enhancement of μ exponent and appearance of the Gaussian ballistic deposition model leads to reduction of structure porosity and enhancement of contour loops area and perimeter. The fractal dimension of the contour set, and the fractal dimension of each loop increases by enhancement of μ exponent. Distributions of loops and geometrical exponents of contour loops in different μ exponent are determined. The results indicate that the hyperscaling relation and Zipf’s law hold for μ≥μc=3 which power-law distributed noise approaches to Gaussian one.

Review of bomb and ash flows: Genesis and case studies of a subset of block and ash flow deposits

Pyroclastic density currents with an abundance of cauliflower-shaped bombs are an uncommon type of deposit, called bomb and ash flow (BoAF) deposits in several papers. Although they are similar to block and ash flow (BAF) deposits (e.g., rich in juvenile blocks and breadcrusted bombs), they are often related to eruptions of mafic to intermediate magmas. In the current study, we analyze and compare historical and prehistorical BoAF-generating eruptions at Asama and Aso (Japan), Mayon (Philippines), Mt. Spurr (United States), Fuego (Guatemala), Arenal (Costa Rica), Cotopaxi and Tungurahua (Ecuador), and Láscar and Tilocálar volcanoes (Chile). Our review indicates that BoAFs show a substantial contribution of juvenile rounded material but with different rheologies and fragmentation mechanisms. This juvenile material is typically basaltic or andesitic, as it is more susceptible to form volcanic bombs with scoriaceous cauliflower textures. Thus, BoAFs could be a subset of the BAF deposits. The study and recognition of this type of deposit in volcanic sequences could be misinterpreted as a ballistic bomb deposit or even a hot bomb-rich lahar deposit, therefore, its appropriate interpretation is fundamental for volcanic hazard assessment.

Scaling limit of the heavy tailed ballistic deposition model with p-sticking

Scaling limit of the heavy tailed ballistic deposition model with p-sticking

Simulation research on surface growth process of positive and negative frequency detuning chromium atom lithographic gratings

Chromium atom photolithography gratings are a promising technology for the development of nanoscale length standard substances due to their high accuracy, uniformity, and consistency. However, the inherent difference between the interaction of positive and negative frequency detuning standing wave field and the atoms can cause a difference in the adjacent peak-to-valley heights of the grating in positive and negative frequency detuning chromium atom lithography, which greatly reduces its accuracy. In this study, we performed a controlled variable growth simulation using the semi-classical theoretical model and Monte Carlo method with trajectory tracking and ballistic deposition methods to investigate the influence of key experimental parameters on the surface growth process of positive and negative frequency detuning atomic lithography gratings. We established a theoretical model based on simulation results and summarized empirical equations to guide the selection of experimental parameters. Our simulations achieved uniform positive and negative frequency detuning atomic lithography gratings with a period of 1/4 of the wavelength corresponding to the atomic transition frequency, and adjacent peak-to-valley heights differing by no more than 2 nm, providing an important theoretical reference for the controllable fabrication of these gratings.

Porosity and conductivity in ballistic deposition with power-law distributed noise

The ballistic deposition model of rod-like particles with power-law distributed noise is studied by the Monte Carlo simulation. In this modified model instead of particles with fixed unit sizes, vertical rods whose length follows the power-law distribution [Formula: see text] are deposited, where [Formula: see text] denotes the power-law strength exponent. This deposition leads to porous rock structures with varying porosity and conductivity. The time evolution of the surface roughness and the porosity of the resulting structures are studied. The conductivity of the structures is calculated using the parallel resistors in the percolation model using a random walk algorithm. Finally, we discuss the relation between porosity, conductivity and the strength exponent of the power-law noise. The results show that the surface roughness increases as a pseudo-step function versus deposition time for [Formula: see text], which leads to an observable reduction in porosity and conductivity. By increasing the [Formula: see text] exponent, the growth exponent of [Formula: see text] for the Gaussian model appears. The conductivity increases as [Formula: see text] versus porosity, [Formula: see text], and remains constant for [Formula: see text] which the value of [Formula: see text] has been identified for BD.

Nanostructured nickel films by supersonic cluster beam deposition: Morphology, oxidation, and clues of hollow structures by Kirkendall effect at room temperature

Supersonic Cluster Beam Deposition was exploited to study morphology, nanostructure and room temperature spontaneous oxidation of Nickel films obtained by cluster assembling in high-vacuum conditions. Size analysis shows the dominant presence of particles with dimensions below 10 nm, while the lognormal profile of the size distribution confirms that gas-phase homogeneous nucleation and aggregation prior to deposition is at the base of the mechanism governing clusters formation. The relationship between surface roughness and film thickness is found to follow a power law, suggesting a growth process ascribable to ballistic deposition model. Although ultrafine dimensions, clusters oxidation is not complete as residual metallic Nickel, beside NiO and Ni(OH)2, is detected by Electron Spectroscopy and observed by Transmission Electron Microscopy and Electron Diffraction, within core-shell structures. Cubic symmetry is identified in both metallic and NiO phases, while hydroxide phase appears as amorphous. The presence of hollow particles is also unveiled, which may represent a first clue of room temperature Kirkendall effect in ultrafine Nickel particles produced by Supersonic Cluster Beam Deposition. The coexistence of core-shell and hollow structures of the same size suggests that particle dimension per-se is not enough to define unambiguously the outcomes of room temperature oxidation process.

Hydrovolcanic eruptions of the Paraná Igneous Province: Insights from mafic volcaniclastic deposits in Sertanópolis, Paraná, Brazil

In many continental flood basalt provinces (CFBPs), primary volcaniclastic deposits formed by explosive hydrovolcanism have been shown to be significant counterparts of better-known effusive facies, a notion that challenged traditional views of CFB evolution. For a long time, the only exception to this was the Paraná Igneous Province in South America. In order to better characterize and understand this setting, detailed geological mapping and petrographic studies were carried out on interflow beds at Sertanópolis, a 250 km2 region in northwest Paraná. Four interflow units were identified at the transition between the high and low TiO2 volcanic sequences. Fine-grained interflow facies include vesiculated clastic rocks, with structures ranging from diffuse to well defined stratification, decimeter-scale dune-bedding with preserved backset and foreset laminations. They are formed mainly by fine accessory (non-juvenile) siliciclastic ash (20–70%) and extremely fine ash or mud (10–50%), followed by fine hydrothermal mica (<5–40%), commonly hydrated (clay-mineral-rich) ash aggregates (<5–20%) and lesser amounts of juvenile and accessory glass and basalt fragments (ash to block-sized, <5–30%). In the eastern portion of the research area, a 4 × 2.5 km region with outcrops of scoriaceous basaltic breccias was mapped. These are mainly matrix to clast-supported breccias with finely laminated matrix similar to the fine-grained units. These rocks are interpreted as accessory-rich mafic pyroclastic beds, and their features suggest that multiple pyroclastic density currents (PDCs) formed each interflow unit, with minor discrete fallout contribution in medial successions. Pyroclastic breccias represent proximal PDC and ballistic deposits that help outline a possible conduit in which magmatic-like fragments are dominant in the framework. Stratified tuff-breccia strata in medial deposits represent progressive dilution of PDCs and continuous reworking of scoriaceous fragments by multiple currents. The local stratigraphy is consistent with repeated explosive hydrovolcanic eruptions in a maar-diatreme-like system similar to hydromagmatic volcanoes of other CFBPs.

The Brownian Castle

AbstractWe introduce a 1+1‐dimensional temperature‐dependent model such that the classical ballistic deposition model is recovered as its zero‐temperature limit. Its ∞‐temperature version, which we refer to as the 0‐Ballistic Deposition (0‐BD) model, is a randomly evolving interface which, surprisingly enough, does not belong to either the Edwards–Wilkinson (EW) or the Kardar–Parisi–Zhang (KPZ) universality class. We show that 0‐BD has a scaling limit, a new stochastic process that we call Brownian Castle (BC) which, although it is “free”, is distinct from EW and, like any other renormalisation fixed point, is scale‐invariant, in this case under the 1:1:2 scaling (as opposed to 1:2:3 for KPZ and 1:2:4 for EW). In the present article, we not only derive its finite‐dimensional distributions, but also provide a “global” construction of the Brownian Castle which has the advantage of highlighting the fact that it admits backward characteristics given by the (backward) Brownian Web (see [37, 16]). Among others, this characterisation enables us to establish fine pathwise properties of BC and to relate these to special points of the Web. We prove that the Brownian Castle is a (strong) Markov and Feller process on a suitable space of càdlàg functions and determine its long‐time behaviour. Finally, we give a glimpse to its universality by proving the convergence of 0‐BD to BC in a rather strong sense. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Large-scale kinetic roughening behavior of coffee-ring fronts.

We have studied the kinetic roughening behavior of the fronts of coffee-ring aggregates via extensive numerical simulations of the off-lattice model considered for this context [Dias et al., Soft Matter 14, 1903 (2018)1744-683X10.1039/C7SM02136D]. This model describes ballistic aggregation of patchy colloids and depends on a parameter r_{AB} which controls the affinity of the two patches, A and B. Suitable boundary conditions allow us to elucidate a discontinuous pinning-depinning transition at r_{AB}=0, with the front displaying intrinsic anomalous scaling, but with unusual exponent values α≃1.2,α_{loc}≃0.5,β≃1, and z≃1.2. For 0<r_{AB}≤1, comparison with simulations of standard off-lattice ballistic deposition indicates the occurrence of a morphological instability induced by the patch structure. As a result, we find that the asymptotic morphological behavior is dominated by macroscopic shapes. The intermediate time regime exhibits one-dimensional KPZ exponents for r_{AB}>0.01 and the system suffers a strong crossover dominated by the r_{AB}=0 behavior for r_{AB}≤0.01. A detailed analysis of correlation functions shows that the aggregate fronts are always in the moving phase for 0<r_{AB}≤1 and that their kinetic roughening behavior is intrinsically anomalous for r_{AB}≤0.01.

Low-albedo asteroids: analogues with a high polarization at large phase angles

ABSTRACT While remote observations of the linear polarization of five low-albedo near-Earth asteroids are available at large phase angles, space missions have collected materials from the surface of two of them and one of them is already back to Earth. The structure of the regolith on the surface may be different from that encountered on larger objects, because of their low gravity and thermal stress cycling. Dust particles crushed from low-albedo meteorites (i.e. Orgueil and Allende) are tentatively used as analogues to provide a better approach of such regoliths. The PROGRA2 experiment studies the light-scattering properties of dust particles of various size distributions under Earth’s gravity either deposited or with clouds lifted by an air-draught, as well as under μ-gravity conditions. Similar maximum in polarization (i.e. Pmax) values are obtained experimentally for dark particles deposited or in levitation, showing that multiple scattering is negligible. The increased sensitivity of PROGRA2 instruments, together with imaging techniques, makes it possible to study Pmax with increasing sizes of the lifted particles, up to mm-sizes and above. Our results confirm that particles constituting the regolith are mm-sized and may reach polarization values up to 50 per cent in good agreement with remote observations. Some materials are also suggested to be present on the surface of the particles. Also, huge agglomerates made by random ballistic deposition may be considered as relevant analogues e.g. for pebbles and boulders.

Existence of stationary ballistic deposition on the infinite lattice

AbstractBallistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically. In this model, blocks of size one fall independently as Poisson processes at each site on the ‐dimensional lattice, and either attach themselves to the column growing at that site, or to the side of an adjacent column, whichever comes first. It is not hard to see that if we subtract off the height of the column at the origin from the heights of the other columns, the resulting interface process is Markovian. The main result of this article is that this Markov process has at least one invariant probability measure. We conjecture that the invariant measure is not unique, and provide some partial evidence.

Superconcentration in surface growth

Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept—called subroughness—meaning that there exist two distinct points such that the expected squared difference between the heights at these points grows sublinearly in time. The main result of the paper is that superconcentration is equivalent to subroughness in a class of growing random surfaces. The result is applied to establish superconcentration in a variant of the restricted solid‐on‐solid (RSOS) model and in a variant of the ballistic deposition model, and give new proofs of superconcentration in directed last‐passage percolation and directed polymers.

In situ measurements of tetrahydrofuran hydrate and ice growth in the presence of copper surface with fringe projection: Growth kinetics and interfacial morphology

In recent years, study on the gas hydrate in the presence of solid surfaces has attracted much interest due to the importance of hydrate deposition on the pipe wall and shutdown of these pipelines. The present work examined the in situ and online monitoring of tetrahydrofuran (THF) hydrate and ice growth on a solid surface using a high-resolution interferometry method. Michelson interferometer was applied to directly measure the thickness of ice and hydrate films using the fringe-shifting technique. Furthermore, the change in the interface morphology during hydrate growth was developed as a function of distortion in the fringe intensity distribution in terms of universal scaling laws. Universal exponent β for the growing interface of THF hydrate was experimentally studied and reported for the first time. Dynamic exponent β was derived as 0.2042, which is in general agreement with other experimental studies of local growth processes. Further, the value of the growth exponent β for the ice growth was obtained by 0.2971, which is close to the value predicted by ballistic deposition and Eden models. Based on the measured dynamic exponents, we suggest that THF hydrate and ice growth can lead to self-similar morphologies and be classified according to their dynamical behavior.

Porosity and Conductivity in Ballistic Deposition with Power-Law Distributed Noise

Porosity and Conductivity in Ballistic Deposition with Power-Law Distributed Noise

Porosity and Conductivity in Ballistic Deposition with Power-Law Distributed Noise

Porosity and Conductivity in Ballistic Deposition with Power-Law Distributed Noise