Power-law Curve Research Articles

Bubble Lifecycle During Heterogeneous Nucleate Boiling

Heterogeneous nucleate boiling over a flat surface has been studied through complete numerical simulations. During the growth and departure of the vapor bubble, the interface is tracked following a coupled level-set and volume of fluid approach. A microlayer evaporation model similar to Sato and Niceno [“A depletable microlayer model for nucleate pool boiling,” J. Comput. Phys. 300, 20–52 (2015)] has been deployed in this investigation. A detailed study of the changes in microlayer structure as a result of different modes of boiling scenario has been performed. The departure diameter is found to increase with an increase in substrate superheat. The predicted departure diameter has been compared with the available experimental and analytical results. A power-law curve has been obtained for depicting the growth rate of bubble depending on the degree of superheat at the wall. The space–time averaged wall-heat flux at different values of superheat temperature of substrate is obtained. Bubble growth during subcooled boiling at a low and intermediate subcooled degree has been observed through direct numerical simulations. The variations in bubble dynamics after departure in saturated and subcooled liquid states have been compared.

Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow

A fundamental and widely applied concept used to study surface flow processes is the advance-time curve, which indicates the time at which water arrives at any given distance along a field length. The advance-time curve is typically characterized by an empirical power law with an exponent r and a numerical prefactor p (i.e., x=ptr). In the literature, different values of r have been reported for various situations and types of surface irrigation. Invoking concepts from percolation theory, a theoretical approach from statistical physics for quantifying transport properties in complex systems, we relate the exponent r to the backbone fractal dimension Db (r = 1/Db). The backbone, through which transport occurs predominantly in a system, is formed by multiply connected loops composed of several paths that bring fluid from an initial point to a final point. The backbone fractal dimension Db, characterizing the complex structure of the backbone, depends on two factors: dimensionality of the system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation with/without trapping). We show that the theoretical bounds of Db are well in agreement with experimental ranges of r reported in the literature for two furrow and border irrigation systems. We further use the value of Db from the optimal path class of percolation theory to estimate the advance-time curves of four furrows and seven irrigation cycles (i.e., 28 experiments). The optimal path is the most energetically favorable path through a system. Excellent agreement was obtained between the estimated and observed curves. We also discuss the indirect effects of initial water content, inflow rate, surface slope, and infiltration rate (soil texture) on system dimensionality, percolation class and, consequently, the backbone fractal dimension value. More specifically, we postulate that for closely-spaced furrows with steep slopes, low infiltration rates, and relatively high inflow rates, the wetting front advance will be mostly quasi one-dimensional. Since the backbone fractal dimension in one dimension is 1, one should expect the exponent r to be near 1.

Transport AC loss in YBCO coated conductor with transverse crack

The purpose of the experiments presented here is to explore the transport alternating current (AC) losses in YBa2Cu3O7−x coated conductor (YBCO CC) that contains a transverse crack. The experimental tests are performed using an improved local calorimetry method with high accuracy. We define a factor called c to describe the ratio between the AC losses of the specimen with and without the crack in terms of unit length. It is found that a power law curve between c and the crack length L coincides perfectly with the experimental results. In addition, we also find that the AC losses in the crack region are hysteretic losses.

Granularity of the top 1,000 Brazilian companies

“Granularity” refers to the fact that economies are populated by a few large companies (the big “grains”) that coexist with many smaller companies. Such a distribution of firm sizes is modeled by power laws. This study adds to the international evidence of the granularity hypothesis by considering data for the top 1,000 Brazilian companies. We sort the companies from top to bottom in terms of their net revenues. Then, we adjust power laws to the data and estimate Pareto and Gumbel exponents. We find we cannot dismiss the hypothesis of granularity for the Brazilian companies. We also find the Pareto exponent is approximately one (1.070 ± .015), roughly a Zipf’s law. Such a result is in line with the previous one found for American companies where the Pareto exponent = 1.059. We also find a power-law progress curve best fits the data.

Characterization of Ivoclar Vivadent Dental Restoration Material for 137CS Retrospective Radiation Dosimetry.

Retrospective dosimetry is the method of using materials on or near a person who is exposed to ionizing radiation to determine the amount of radiation received by the person. A possible candidate material for retrospective dosimetry is Ivoclar Vivadent IPS e.max® CAD ceramic dental restoration material, which exhibits radiation-induced thermoluminescence when exposed to gamma- and x-ray radiation from a Cs source. The purpose of this paper is to characterize the material and study the behavior of the thermoluminescence signal with radiation dose and with delay time between radiation exposure and thermoluminescence measurement. The first glow peak is well-modeled by a first-order glow curve deconvolution formula. The height of the first glow peak is approximately linear with dose. The fading of the signal with time is approximately described by a power law curve with cutoff. The material appears to be suitable for retrospective radiation dosimetry.

Empirical growth models for the renewable energy sector

Abstract. Three simple, empirical models for growth of power consumption in the renewable energy sector are compared. These are the exponential, logistic, and power-law models. The exponential model describes growth at a fixed relative growth rate, the logistic model saturates at a fixed limit, while the power-law model describes slowing, but unlimited, growth. The model parameters are determined by regression to historical global data for solar and wind power consumption, and model projections are compared to scenarios based on macroeconomic modelling that meet the 2∘ target. It is demonstrated that rational rejection of an exponential growth model in favour of a logistic growth model cannot be made from existing data for the historical evolution of global renewable power consumption y(t). It is also shown that the logistic model yields saturation of growth at unrealistic low levels. The power-law growth model is found to give very good fits to the data through the last decade, and the projections align very well with the scenarios. Power-law growth is equivalent to the simple law that the relative growth rate y′/y decays inversely proportional to time. It is shown that this is a natural model for growth that slows down due to various constraints, yet not experiencing the effect of a strict upper limit defined by physical boundaries. If the actual consumption follows the power-law curve in the years to come the exponential-growth null hypothesis can be correctly rejected around 2020.

Assessing glacial modification of bedrock valleys using a novel approach

Analysis of valley cross sections is an established technique for evaluating the effects of glacial erosion. Here, we present a semiautomated approach for assessing glacial modification of bedrock valleys by quantifying morphological variability in valley cross sections extracted in bulk from digital elevation models (DEMs). This method can be tailored to derive cross sections of user-specified width and spacing and can generate cross-sectional data sets of multiple orders of magnitude. We demonstrate the technique by extracting ~27,000 cross sections from the Sierra Nevada, California, and computing measures of valley morphology including a form ratio, a quadratic curve fit, and a power law curve fit for each cross section. In addition, we introduce a novel metric, the V-index, which is calculated by comparing valley cross-sectional area to that of an ideal V-shaped cross section and is, thus, an expression of the deviation from an ideal V-shaped form. Statistical comparisons of the different measures suggest that the V-index is a robust alternative to traditional morphological measures because it can accommodate irregular valley cross sections and discriminate between glacial and nonglacial forms. We document the distribution of valley forms throughout the Sierra Nevada using the V-index to identify range-scale patterns in cross-sectional morphology and to investigate the role of lithology on glacial modification of bedrock valleys.

High-speed bending-fatigue testing of composite materials

A methodology for high-speed fatigue testing, especially for resin materials, including fibre-reinforced composites, was devised and evaluated. To exert periodic stress on a material at a frequency of more than 200 Hz, a specimen (made of glass fibre-epoxy laminate) was fixed as a cantilever to an electromagnetic vibrator and vibrated at its resonant frequency of the first bending mode by using a resonance tracking control. The shape of the specimen was designed with finite-element vibration analysis to obtain a resonant frequency of more than 200 Hz and a desired strain distribution for inducing fatigue damage under a certain stress level. The rise in temperature during the fatigue testing (due to damping loss) was estimated by applying heat-transfer theory and suppressed by external cooling to keep the specimen at room temperature. To confirm the validity of the devised high-speed-testing method, a completely reversed bending test at 1 Hz was also performed with identical specimens. The results from both testing methods (conducted at 230 Hz and 1 Hz, respectively) were plotted on a single power-law curve in an S-N plot. The good agreement between the two plots suggests that fatigue strength in the high- or giga-cycle region of resin and composites can be evaluated in a very short time if temperature is controlled appropriately.

Two-Dimensional Thickness-Dependent Avalanche Breakdown Phenomena in MoS2 Field-Effect Transistors under High Electric Fields.

As two-dimensional (2D) transition metal dichalcogenides electronic devices are scaled down to the sub-micrometer regime, the active layers of these materials are exposed to high lateral electric fields, resulting in electrical breakdown. In this regard, understanding the intrinsic nature in layer-stacked 2D semiconducting materials under high lateral electric fields is necessary for the reliable applications of their field-effect transistors. Here, we explore the electrical breakdown phenomena originating from avalanche multiplication in MoS2 field-effect transistors with different layer thicknesses and channel lengths. Modulating the band structure and bandgap energy in MoS2 allows the avalanche multiplication to be controlled by adjusting the number of stacking layers. This phenomenon could be observed in transition metal dichalcogenide semiconducting systems due to its quantum confinement effect on the band structure. The relationship between the critical electric field for avalanche breakdown and bandgap energy is well fitted to a power law curve in both monolayer and multilayer MoS2.

Damköhler number-based research on dividing dissolution patterns in carbonate acidizing

In general, the main dissolution patterns in carbonate acidizing include face dissolution, wormhole dissolution and uniform dissolution. Wormholes can also be divided into single, dominant wormhole, ramified wormhole and so on. The wormholes can establish advantageous channels for oil and gas in the reservoirs, increase the permeability of formations and achieve the ultimate goal of carbonate matrix acidizing. Considering the factors that affect carbonate acidizing, the flow rate of acid plays the key role in determining dissolution patterns. Many scholars have carried out the researches by means of numerical simulation or physical simulation experiment individually, but the reports which combine the two methods and define the flow rate boundary between different dissolution patterns in carbonate acidizing are rare. In this paper, the flow rate of acid was dimensionless on the basis of Damköhler number (Da), and the boundary of acid injection rate was confirmed by combining numerical simulation with physical simulation experiments. Among the various types of dissolution models, the two-scale continuum model comprehensively considers the convection, diffusion and acid-rock interfacial reaction and is capable of dynamically monitoring the acidizing region at different time steps. This paper, using the finite difference method, solved the typical two-scale continuum model. In order to extend the calculation of the range of Damköhler number, Steffensen's acceleration method was applied to the porosity variation equation. The previous conclusion that at higher injection rate the breakthrough pore volume of acid is in direct proportion to the one-third power of the average pore velocity was validated. Furthermore, the typical pressure fall-off curve was analyzed. Results show that the typical pressure drop curve changes from the power-law curve to the straight line, as the injection rate decreases. Based on the analysis of porosity field and concentration field, combined with physical simulation experiment, the change law of dissolution pattern with Da was analyzed, which clarify the injection rates boundary of dissolution pattern. The results show when Da is between 50 and 200, the core appears wormholes, when Da is between 1 and 50, the dissolution pattern is the transition stage from wormhole to uniform dissolution and when Da is between 200 and 500, the core dissolution pattern is the transition stage from wormhole to face dissolution. The Damköhler number and injection rates of different dissolution patterns can be used to guide the design of acidizing construction.

Effects of crude oil contamination on soils of the Ural region

Nowadays, crude oil contamination of soil is one of the widespread environmental problems. In this paper, we examine the impact of oil contamination on individual components of soil ecosystems at the physicochemical and biological levels. We investigated the hydrophysical properties, benzo[a]pyrene content, phytotoxicity, and toxicity for test organisms (Daphnia magna Straus, Escherichia coli) of the experimental crude oil-contaminated soils. The effects of the different levels of crude oil contamination of soil ecosystems on hydrophysical parameters, vegetative growth, the dynamics of microbial degradation of the benzo[a]pyrene, and level of toxicity to organisms of the different taxonomic groups have been examined. The findings indicate that the dependency of change in capillary moisture capacity upon concentration of crude oil is linear and the change of water absorption and infiltration time follows the power-law growth curve. Oil contamination affects the conditions of vegetative growth non-linearly. The floral component of a mixed coniferous-broad-leaved forest ecosystem is less susceptible to crude oil exposure than the floral component of the southern taiga. Varied dynamics of the microbial degradation of one of the chemical components of crude oil hydrocarbons (benzo[a]pyrene) in soil ecosystems at intervals of 40–100-g/kg of soil and 200–300-g/kg of soil was established. The soil becomes acutely toxic with oil concentration exceeding 200 g/kg of soil for animals (test organism D. magna Straus), and 40 g/kg of soil and 200 g/kg of soil for bacteria (test organism E. coli). The most disastrous effects occur when oil doses exceed 200 g/kg of soil. The study of hydrophysical and biological features of experimentally oil-contaminated soils of the Ural region added a new dimension to our knowledge about the impact of crude oil contamination on individual elements of ecosystems.

On notch and crack size effects in fatigue, Paris’ law and implications for Wöhler curves

As often done in design practice, the Wohler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0 (of the order of 10-103), and the fatigue limit at a “infinite life”, also conventional, typically N∞=2·106 or N∞=107 cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/DKth, and static strength to endurance limit, FR =sR /Ds0, qualitative trends are obtained for the finite life region. Paris’ and Wohler’s coefficients fundamentally depend on these two ratios, which can be also defined “sensitivities” of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Wohler coefficient, k’, is found as a function of the intrinsic Wohler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k<k’<m, as a function of size of the notch: in particular, k’=k holds for small notches, then k’ decreases up to a limiting value (which depends upon Kt for mildly notched structures, or on FK and FR only for severe notch or crack). A perhaps surprising return to the original slope k is found for very large blunt notches. Finally, Paris’ law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, Paris’ coefficient m is coincident with the limiting value of k’lim. The scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole–Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log–log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Hot Deformation Behavior of Four Steels: A Comparative Study

The hot deformation behavior of four different steels in the as-cast condition was investigated by means of hot compression tests conducted at temperatures ranging from 1100 °C up to 1200 °C, and at strain rates in between 0.12 and 2.4 s−1. The primary focus of this work was to check the possibility to increase the strain rate during the rough preliminary working of the ingots, i.e., to adopt a rough rolling process in place of the more conventional rough forging. The second aim of the research was to study the influence of the different characteristics of these steels in their as-cast conditions on their hot deformation behavior. It was seen that in all deformation conditions, the stress–strain compression curves show a single peak, indicating the occurrence of dynamic recrystallization (DRX). The hot deformation behavior was studied in both the condition of dynamic recovery (DRV), modeling the stress–strain curves in the initial stage of deformation, and DRX. Data of modeling were satisfactorily employed to estimate the flow stress under different conditions of temperature and strain rate. The experimental values of the activation energy for hot deformation, QHW, were determined and correlated to the chemical composition of the steels; a power law curve was found to describe the relation of QHW and the total amount of substitutional elements of the steels. The critical strain for DRX, εc, was determined as a function of the Zener–Hollomon parameter and correlated to the peak strain, εp. A ratio εc/εp in the range 0.45–0.65 was found, which is in agreement with literature data. All this information is crucial for a correct design of the rough deformation process of the produced ingots.

Longitudinal development of flow-separation lines on slender bodies in translation

This paper examines flow-separation lines on axisymmetric bodies with tapered tails, where the separating flow takes into account the effect of local body radius $r(x)$, incidence angle $\unicode[STIX]{x1D713}$ and the body-length Reynolds number $\mathit{Re}_{L}$. The flow is interpreted as a transient problem which relates the longitudinal distance $x$ to time $t^{\ast }=x\,\text{tan}(\unicode[STIX]{x1D713})/r(x)$, similar to the approach of Jeans &amp; Holloway (J. Aircraft, vol. 47 (6), 2010, pp. 2177–2183) on scaling separation lines. The windward and leeward sides correspond to the body azimuth angles $\unicode[STIX]{x1D6E9}=0$ and $180^{\circ }$, respectively. From China-clay flow visualisation on axisymmetric bodies and from a literature review of slender-body flows, the present study shows three findings. (i) The time scale $t^{\ast }$ provides a collapse of the separation-line data, $\unicode[STIX]{x1D6E9}$, for incidence angles between $6$ and $35^{\circ }$, where the data fall on a power law $\unicode[STIX]{x1D6E9}\sim (t^{\ast })^{k}$. (ii) The data suggest that the separation rate $k$ is independent of the Reynolds number over the range $2.1\times 10^{6}\leqslant \mathit{Re}_{L}\leqslant 23\times 10^{6}$; for a primary separation $k_{1}\simeq -0.190$, and for a secondary separation $k_{2}\simeq 0.045$. (iii) The power-law curve fits trace the primary and secondary lines to a characteristic start time $t_{s}^{\ast }\simeq 1.5$.

Feasibility of electricity generation using WECS in the selected locations of Tigray region (Ethiopia)

This paper presents the feasibility of electricity generation using WECS in the selected locations of Tigray region in Ethiopia. Weibull parameters were obtained using the energy pattern factor method (EPFM). A linear agreement was observed between mean wind speed and power density. Analysis of the present value of cost per kilowatt hour was estimated for selected wind turbines at different hub heights. In addition, regardless of the location, power law curve fit provides higher regression than the linear curve fit. From the analysis of results and discussion, it is revealed that (WECS)III has the least progressive ratio when compared with (WECS)IV. Finally, the average specific cost per unit for all chosen turbines at Mekele and Chercher is comparable to the cost per kWh charged by EEPCo, except for a few turbines in this study.

Development of a stress-based creep-fatigue equation: Accommodating pure-fatigue to pure-creep for the high-cycle loading regime

Background The creep-fatigue damage in low-cycle regime has been described by a strain-based creep-fatigue equation through integrating creep effect into fatigue damage. Need There is a need to develop a creep-fatigue equation which describes the stress-controlled creep-fatigue behaviour in high-cycle regime. Approach This stress-based creep-fatigue equation was developed through superposing a fatigue mechanism with a creep mechanism. This creep-fatigue equation was then validated on GP91 casting steel. The creep-fatigue data were transformed to the reference condition and collapsed into one power-law curve with good quality. Outcomes This result verified the formulas of the fatigue component and the creep component, and demonstrated the method of extracting the coefficients. The full-range characteristic of this creep-fatigue equation is discussed. In addition, the introduction of the compatibility presents a better description of the reference condition. Originality A new creep-fatigue equation is provided with demonstrably good ability to cover the full range of conditions from the pure-fatigue condition to the pure-creep condition for the high-cycle regime. The method of extracting the coefficients is also provided.

High-fidelity modeling and numerical simulation of cratering induced by the interaction of a supersonic jet with a granular bed of solid particles

The dynamics of cratering caused by a supersonic jet on a granular bed of solid particles is investigated using a high fidelity, two-phase model and numerical simulations. To model the gas phase, the Large Eddy Simulation (LES) approach is used and a kinetic theory based model is employed for the solid phase. Three-dimensional time-dependent simulations are conducted for the purpose of elucidating the morphological features of the crater and their evolution with time. Parametric variations of the initial conditions are performed to understand the effect of the initial solid volume fraction in the bed, of the coefficient of restitution, of the jet Mach number, of the particle diameter, and of the particle material density. Simulation snapshots of the craters are in qualitative agreement with images from the Mars Science Laboratory (MSL) mission and from Earth-based experiments. Analysis of the results shows that solid particle compaction at the crater base and side walls increases with increasing volume fraction of the undisturbed particle bed and reaches solid volume fractions close to 0.65. The coefficient of restitution is shown to have no effect on the large scale dynamics of the crater but affects the small scale features, particularly the shape of elongated bursts of solid particle clouds as well as radially aligned structures on the outer crater walls. A smaller jet Mach number results in a smaller crater characterized by ridge-like structures and walls at an angle of approximately 45° with respect to the undisturbed bed whereas larger Mach number jets create craters with walls approximately perpendicular to the undisturbed bed. A smaller particle size and a lighter particle material density also result in wider and deeper craters. The formation of all morphological structures is explained in detail and is related to the physical phenomena from which they originate. Power law curve fits are also presented for the crater outer diameter as well as for the depth. The mean and rms profiles of the solid volume fraction are computed, and it is found that the peak rms in the solid volume fraction does not occur at the surface but rather in the depth of the crater. In addition, the mean and rms of the particle momentum flux are also computed and discussed. Furthermore, the sources of particle momentum are evaluated, and the viscous drag as well as the gas pressure gradient are observed to be the prominent effects. The results show that the model developed is robust and is able to simulate craters due to a range of external conditions operating over particle beds having different characteristics.

Measurement of air void system in lightweight concrete by X-ray computed tomography

An industrial lightweight concrete developed for pipe insulation is characterized using X-ray computed tomography to determine the size distribution of air voids within the paste fraction. Strategies to address practical difficulties are presented, particularly discerning air voids in paste from air voids within aggregate, and combining air void size distribution data collected at different resolutions. To address the first issue, a step-wise approach was employed to reduce the problem to a series of easier-to-solve two-phase grayscale threshold problems. The first step isolates a significant number of light weight aggregate particles on 2D slices using an active contour line approach and an effective threshold identified to discern between air void and solid voxels. The threshold is applied globally to the 3D data set, and the air void voxels removed. Next, a significant number of rectangular regions of interest from 2D slices are used to identify a second threshold between the solid portions of the lightweight aggregate and the paste. Finally, a 3D shape based criterion is used to isolate air voids in paste. Given the trade-off between resolution and sample size, it is necessary to conduct multiple scans using different resolutions and sample diameters in order to cover the full range of the air void size distribution. A power law curve is used to unite distributions collected at different resolutions.

Boulder abundances and size-frequency distributions on Oxia Planum-Mars: Scientific implications for the 2020 ESA ExoMars rover

This paper presents the abundances and the size-frequency distributions (SFD) of boulders identified on a sector of the prime landing site for the ExoMars 2020 rover, in Oxia Planum region. By means of a HiRISE image, boulders≥ 1.75m across have been identified and subdivided according to the two main Oxia Planum geological units: the Noachian clay-rich formation (Nc), and the Amazonian volcanic deposit (Av).The spatial density of boulders≥ 1.75m over the entire study area is 6.75 × 10−4/m2, with a size-frequency that is best fit both with power-law and exponential-law curves with indices of −4.9 + 0.1/−0.2 and −1.29 + 0.04/−0.06 respectively. Significant differences were found by analysing separately the Av and Nc geological units. The data collected in the Av unit are well-fitted with a power-law curve with an index equal to −4.8 +/−0.2 and with an exponential-law curve with an index of −1.24 + 0.05,−0.06, whilst in the Nc unit such indices are −5.5 + 0.3/−0.4 and −1.70 + 0.09/−0.12 (power-law and exponential-law curve, respectively).The spatial density of boulders in the Av unit is 7.0 times larger than in the Nc one. This may be due primarily to the distinct mechanical properties of the two units that may result in a different production rate or preservation of the boulders. Secondly, the Av unit overlies the Nc unit, possibly resulting in more impacts and/or different weathering processes throughout the ages.This study provides a quantitative evaluation of the abundances of boulders≥ 1.75m across on Oxia Planum: it is therefore a reference for the ExoMars 2020 mission, both during the landing phase and the rover traverse to specific areas of interest. The landing ellipse presents much higher abundances of boulders≥ 1.75m than all previous Martian rover landing areas. This is particularly evident when the rougher Av unit is taken into account. Contrarily, the Nc unit shows a much more comparable value, but still slightly higher, to the Mars Pathfinder landing site. We provide illustrative navigating scenarios for both the Nc and the Av units as well.