Search

The main focus of this article is to study the characteristics of charged pions and their correlation with shower particles emitted in the interaction of 84Kr + emulsion at 1 A GeV. Author have also studied the dependence of the average multiplicity of charged pions and shower particles with projectile mass. In this study author observed that the average multiplicity of charged pions and shower particles showing the linear dependency on the projectile mass.

A high-order numerical manifold method (HONMM) is developed using four-node quadrilateral (QUAD4) element to enhance accuracy and computational efficiency in solid mechanical problems. In the curre...

The exact linear dependency among age, period and birth cohort makes it impossible to recover the true parameters of Age-Period-Cohort (APC) models. We then propose to extract reliable information from APC models via the Shapley decomposition, a model-agnostic procedure from game theory that allows to pin down the most likely contribution of each regressor in explaining the variance of the dependent variable. The rationale is that the predicted values of APC models are estimable and the allocation of the R2 to the APC regressors – interpreted here as the APC “effects” – satisfies desirable properties and produces robust estimates, in that complementing existing methods. We apply the method to the U.S. unemployment rate.

Purpose Magnetization transfer ratio (MTR) histograms are used widely for the assessment of diffuse pathological changes in the brain. For broad clinical application, MTR scans should not only be fast, but confounding factors should also be minimized for high reproducibility. To this end, a 1-minute whole-brain spiral MTR method with intrinsic B1 -field correction is introduced. Methods A spiral multislice spoiled gradient-echo sequence with adaptable magnetization-transfer saturation pulses (angle β) is proposed. After a low-resolution single-shot spiral readout and a dummy preparation period, high-resolution images are acquired using an interleaved spiral readout. For whole-brain MTR imaging, 50 interleaved slices with three different magnetization-transfer contrasts (β = 0°, 350°, and 550°) together with an intrinsic B1 -field map are recorded in 58.5 seconds on a clinical 3T system. From the three contrasts, two sets of MTR images are derived and used for subsequent B1 correction, assuming a linear dependency on β. For validation, a binary spin bath model is used. Results For the proposed B1 -correction scheme, numerical simulations indicate for brain tissue a decrease of about a factor of 10 for the B1 -related bias on MTR. As a result, following B1 correction, MTR differences in gray and white matter become markedly accentuated, and the reproducibility of MTR histograms from scan-rescan experiments is improved. Furthermore, B1 -corrected MTR histograms show a lower variability for age-matched normal-appearing brain tissue. Conclusion From its speed and offering intrinsic B1 correction, the proposed method shows excellent prospects for clinical studies that explore magnetization-transfer effects based on MTR histogram analysis.

Real-world structural optimisation problems involve multiple loading conditions and design constraints, with responses typically depending on states of discretised governing equations. Generally, one uses gradient-based nested analysis and design approaches to solve these problems. Herein, solving both physical and adjoint problems dominates the overall computational effort. Although not commonly detected, real-world problems can contain linear dependencies between encountered physical and adjoint loads. Manually keeping track of such dependencies becomes tedious as design problems become increasingly involved. This work proposes using a Linear Dependency Aware Solver (LDAS) to detect and exploit such dependencies. The proposed algorithm can efficiently detect linear dependencies between all loads and obtain the exact solution while avoiding unnecessary solves entirely and automatically. Illustrative examples demonstrate the need and benefits of using an LDAS, including a run-time experiment.

This work presents the results of an experimental study and thermodynamic study of solar drying of tomatoes of the KAWA type, where the drying experiments was carried out in a large scale mixed solar dryer. The aim is to obtain the drying curves and calculate the effective diffusivity to predict drying kinetics and thermodynamic characteristics of tomatoes drying. The tomato samples were cut in two different shapes namely flat slices and wedges. In the case of flat slices, there were four different thicknesses, 0.5, 1, 1.5, 2 cm. For the wedged slices, the tomatoes was slit into 2, 4, 8 and 16 equal sections. The moisture content of the tomatoes varied between 92.5 and 93.6%. The tomatoes were weighed regularly until moisture content fell between 18 and 25%. The Fick’s diffusion equation was used to calculate the effective diffusivity from the experimental data by fitting a linear dependency. A new proposed approach from the Arrhenius equation and a literature model were used to determine thermodynamic parameters. The drying operation lasted from 5 h to 21.25 h for flat slices and 8.5 h to 28.25 h for the wedges. The thermodynamic parameters derived from the new proposed approach are compared with the literature model. Evidently, the Gibbs free energy values indicate that tomato solar drying is a spontaneous natural process.

The Geant4 simulation toolkit needs to be optimized for central processing unit (CPU) time and memory size in order to be used for a high luminosity Large Hadron Collider (LHC) experiment. We have developed a low-energy physics profiling system and studied Geant4 with respect to both software and hardware. The results of profiling with Geant4 for low-energy physics were provided to the users and developers of the Geant4 simulation toolkit. In the case of the software, we performed profiling for dependence on different Geant4 versions and provided feedback to Geant4 developers. Profiling for dependence on the number of events showed their linear dependency. In the case of the hardware, we performed profiling for machine dependency on the KISTI-4 supercomputer. This action showed that machines were homogenous. The results obtained in this study will serve as a reference for Geant4 users.

ObjectivesThis study investigated the performance and robustness of radiomics in predicting COVID-19 severity in a large public cohort.MethodsA public dataset of 1110 COVID-19 patients (1 CT/patient) was used. Using CTs and clinical data, each patient was classified into mild, moderate, and severe by two observers: (1) dataset provider and (2) a board-certified radiologist. For each CT, 107 radiomic features were extracted. The dataset was randomly divided into a training (60%) and holdout validation (40%) set. During training, features were selected and combined into a logistic regression model for predicting severe cases from mild and moderate cases. The models were trained and validated on the classifications by both observers. AUC quantified the predictive power of models. To determine model robustness, the trained models was cross-validated on the inter-observer’s classifications.ResultsA single feature alone was sufficient to predict mild from severe COVID-19 with and (p<< 0.01). The most predictive features were the distribution of small size-zones (GLSZM-SmallAreaEmphasis) for provider’s classification and linear dependency of neighboring voxels (GLCM-Correlation) for radiologist’s classification. Cross-validation showed that both . In predicting moderate from severe COVID-19, first-order-Median alone had sufficient predictive power of . For radiologist’s classification, the predictive power of the model increased to as the number of features grew from 1 to 5. Cross-validation yielded and .ConclusionsRadiomics significantly predicted different levels of COVID-19 severity. The prediction was moderately sensitive to inter-observer classifications, and thus need to be used with caution.Key pointsInterpretable radiomic features can predict different levels of COVID-19 severityMachine Learning-based radiomic models were moderately sensitive to inter-observer classifications, and thus need to be used with caution

Japanese individuals have a unique culture of soaking in a bathtub, and forensic pathologists have experienced fatal cases due to drowning. However, T1 and T2 relaxation times of a drowning lung are poorly documented. In the present study, we investigated the relationship between drowning water temperature and T1 and T2 relaxation times of drowning lung tissues at 9.4 T MRI (Bruker, BioSpec94/20USR). The mice used as animal drowning models were directly submerged in freshwater. Water temperature was set to 8 °C–10 °C (cold), 20 °C–22 °C (normal), 30 °C, and 45 °C. The regions of interest (ROIs) on the axial section of the third slice were set at the central and peripheral areas of each—the left and the right—lung. T1 relaxation times measured immediately after death differed by the presence or absence of soaking water, except in case of cold water temperature. In the drowning groups, T1 relaxation time showed a linear dependency on water temperature. By contrast, T2 relaxation time was almost constant regardless of the presence of drowning under the same temperature condition; when compared in the lung areas of the same individuals, the times were uniformly reduced in drowning models. To minimize the effects of hypostasis and decomposition, we performed measurements immediately after death and were able to determine the noticeable difference in drowning water temperature. These results may be useful for qualitative assessments of a drowning lung and may serve as a basis when imaging the human body during forensic autopsy cases.

Random effects (RE) models have been widely used to study the contextual effects of structures such as neighborhood or school. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, it has not been fully understood how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater -- not less -- rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect's linear component and the random intercept to be zero. For APC models with two RE's, the effective constraints implied by the model depend on the true (i.e., in the data-generating mechanism) non-linear components of the effects that are modeled as RE's, so that the estimated linear components of the RE's are determined by the true non-linear components of those effects. In conclusion, RE-APC models impose arbitrary though highly obscure constraints and thus do not differ qualitatively from other constrained APC estimators., Submitted to "Sociological Methodology"

Considering the widespread contaminations of food products with mycotoxins, it is important to develop, robust, time- and cost-effective detection methods. We developed and optimized an immunoassay using a continuous flow system for the detection of zearalenone (ZEN). The assay was performed in a flow mode using an automated sequential injection system. Time for an assay cycle was 18 Min. Under optimal conditions, the limit for quantification for ZEN was 0.40 µg L-1 with a linear dependency between concentration and signal amplitude between 0.10 and 10 µg L-1 . The assay proved to be robust and reliable with 13% relative standard deviation between measurements. By dissociating the antigen-antibody complex using a regeneration solution, we showed 50 times reusability of the immobilized antibodies without affecting the antigen-binding properties.

In this chapter we provide two additional facts from linear algebra, namely Linear Dependency Relationship algorithm and a calculation of the Vandermonde determinant. We also derive Stirling’s formula to understand the growth of factorials.

The majority of the operating costs of commercial crushing are caused by the power consumption and the wear part maintenance. Better understanding of the variables affecting the compressive crushing is needed when aiming to lower the operational costs of material comminution. The gouging or high stress wear tests are commonly conducted with laboratory sized jaw or cone crushers that do not allow easy alteration of the movement or geometry of the wear surfaces. Therefore, a new innovative jaw crusher-type wear tester was designed especially for wear and mineral property research. The modular jaws of the developed dual pivoted jaw crusher allows flexible selection of jaw geometry, which is independent of the selectable compressive and sliding movements of the jaws. The narrow jaw design produces extensive wear in the specimens even when small amounts of abrasive are crushed. The reference tests with a structural steel show excellent repeatability of the wear loss and energy measurements during the tests. The results with varying sliding movement of the jaws showed linear dependency between the wear of the jaw plates and energy spent. A method to separate the energy spent in wear from the energy spent in comminution is also described in this paper.

Stewart--Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart--Gough platform is rigid with 40 assembly configurations (over the complex numbers), while exceptional Stewart--Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart--Gough platforms called Segre-dependent Stewart--Gough platforms which arise from a linear dependency of point-pairs under the Segre embedding and compute an irreducible decomposition of this family. We also consider Stewart--Gough platforms which move with two degrees of freedom. Since the Segre embedding arises from a representation of the special Euclidean group in three dimensions which has degree 40, we consider the special Euclidean group in other dimensions and compute spatial Stewart--Gough platforms that move in 4-dimensional space.

One- and two-dimensional materials are being intensively investigated due to their interesting properties for next-generation optoelectronic devices. Among these, armchair-edged graphene nanoribbons are very promising candidates with optical properties that are dominated by excitons. In the presence of additional charges, trions (i.e., charged excitons) can occur in the optical spectrum. With our recently developed first-principle many-body approach (Phys. Rev. Lett. 116, 196804), we predict strongly bound trions in free-standing nanoribbons with large binding energies of 140-660 meV for widths of 14.6-3.6 Å. Both for the trions and for the excitons, we observe an almost linear dependency of their binding energies on the band gap. We observe several trion states with different character derived from the corresponding excitons. Because of the large bindings energies, this opens a route to applications by which optical properties are easily manipulated, for example, by electrical fields.

Increasing of measurement accuracy is always a relevant goal. Applied to cyberphysical systems, it helps to improve their operation and quality of decision-making. One of the methods to achieve this is to use relations between quantities to be measured – if such relationships exist and are known at least approximately. At present, there are not so many published articles that describe metrological applications which use this kind of information about measured quantities to get a better accuracy. It seems that the small amount of practical realizations is due to the necessity to use rather sophisticated mathematical approaches based on the probability theory and mathematical statistics along with numerous simulations to make a conclusion about the potential increase of accuracy. This paper presents a simplified approach producing a set of clear enough equations and indicators, which are helpful for engineers during preliminary estimation of the potential increase of accuracy from the known interconnections between the measured quantities. A case of linear dependency between the measured quantities is analyzed to show how the approach works.

Vitamin D (25(OH)D) insufficiency and deficiency are highly prevalent in adult soccer players and can exceed 80% even in regions with high insolation, however, the treatment of this condition is often complicated. The aim of the present study was to examine the prevalence of vitamin D insufficiency and deficiency in youth Russian soccer players and the efficacy of its treatment. Participants were 131 young male football players (age 15.6 &plusmn, 2.4 years). Low vitamin D levels (below 30 ng/mL) were observed in 42.8% of the analyzed participants. These athletes were split in two groups composed of persons with vitamin D deficiency (serum vitamin D below 21 ng/mL) and insufficiency (serum vitamin D in range of 21&ndash, 29 ng/mL). A dietary supplement of 5000 IU cholecalciferol per day was administered for two months. After the treatment, an average 92% increase in vitamin D concentration was observed (before treatment&mdash, 19.7 &plusmn, 5.4 ng/mL, after treatment&mdash, 34.7 &plusmn, 8.6 ng/mL, p&lt, 0.001) and 74% of the post-treatment values were within the reference range (30&ndash, 60 ng/mL). Serum concentration of vitamin D increased by 200% &plusmn, 98% (p&lt, 0.001) during the first month of treatment with vitamin D deficiency and insufficiency being successfully treated in 83% of the football players. In summary, the prevalence of vitamin D insufficiency and deficiency was high in young Russian soccer players. Furthermore, it was indicated that the daily usage of cholecalciferol in a dose 5000 IU was an effective and well-tolerated treatment for vitamin D insufficiency. No linear dependency between the duration of treatment and increase in vitamin 25(OH)D concentration was observed.

The Acute Medical Admission Unit (AMAU) model of care has been widely deployed, we examine changes in hospital readmission rates, length of stay (LOS) and 30-day in-hospital mortality over 16 years.All emergency medical admissions between 2002 and 2017 were examined. We assessed 30-day in-hospital mortality, readmission rates, and LOS using logistic regression and margins statistics modelled outcomes against predictor variables.There were 106,586 admissions in 54,928 patients over 16 years. Calculated per patient the 30-day in-hospital mortality was 8.9% (95%CI 8.6% to 9.2%) and showed a relative risk reduction (RRR) of 61.1% from 12.4% to 4.8% over the 16 years (p = .001). Calculated per admission the 30-day in-hospital mortality was 4.5% (95%CI 4.4% to 4.6%) with a RRR of 31.9% from 2002 to 2017. Over this extended period 48.7% of patients were readmitted at least once, 9.3%5 times and 20 patients50 times each. The median LOS was 5.9 days (IQR 2.4, 12.9) with no trend of change over time. Total readmissions increased as a time dependent function; early readmissions (4 weeks) fluctuated without time trend at 10.5% (95%CI 9.6 to 11.3). A logistic regression model described the hospital LOS as a linear function both of comorbidity and the utilisation of inpatient procedures and services.30-day in-hospital mortality showed a linear trend to reduce over time at unaltered LOS and readmission rates. LOS showed linear dependency on clinical complexity; interventions aimed at reducing LOS may not be appropriate beyond a certain point.

A method is proposed for the calculation of bulk viscosity, μ_{b}, of dilute gases using nonequilibrium molecular dynamics (NEMD) simulations. The method uses measurement of mechanical (P_{mech}) and thermodynamic pressure (P_{thermo}) in a NEMD simulation of an expanding fluid and then relates the bulk viscosity to them by the relation μ_{b}=(P_{mech}-P_{thermo})/∇·u[over ⃗], where ∇·u[over ⃗] is the controlled rate of expansion of the fluid per unit volume. A special emphasis is given to the fundamental physical understanding of bulk viscosity in this work. The proposed method is demonstrated for the estimation of bulk viscosity of dilute nitrogen gas in the temperature range of 200-800 K. Variation of bulk viscosity with temperature is reported in the above-mentioned temperature range and is found to be in a reasonably good agreement with the data available in the literature. Furthermore, variation of bulk viscosity with pressure and volumetric expansion rate is obtained. A weak linear dependency of bulk viscosity with pressure is observed, which increases with temperature. However, no significant effect of the rate of volumetric expansion is observed until 10^{8}s^{-1}. Moreover, the effect of the direction of volumetric change (expansion vs. compression) is also demonstrated in this work.

FeCrAl oxide-dispersion-strengthened (ODS) alloys are promising materials for accident tolerant fuels for light water reactors (LWRs). In these alloys, Al and Cr are key elements with important synergistic effects: enhancement of the formation of oxidation-resistant Al2O3 phase by Cr addition and suppression of the formation of the embrittling Cr-rich α′ phase by Al addition. The solid-solution strengthening resulting from Al and Cr co-addition was investigated in this study. The Al and Cr contents were systematically varied from 9 to 16 at.% and 10–17 at.%, respectively, and tensile tests were conducted at 298 K, 573 K, and 973 K. The solid-solution strengthening increased linearly, 20 MPa per 1 at.% Al and 5 MPa per 1 at.% Cr, at the typical LWR operational temperature of 573 K. The conventional Fleischer–Friedel and Labusch theories cannot explain this level of solid-solution strengthening. It was originally clarified that the solid-solution strengthening by Al and Cr in the FeCrAl-ODS alloys can be reasonably predicted by modifying shear modulus difference for the Suzuki's double kink theory for screw dislocations. The inverse dependency on the absolute temperature and linear dependency on the Al and Cr content can be successfully realized by this approach.

Purpose: This work examines the subject of contrast-to-noise ratio (CNR), specifically between tumor and tissue background, and its dependence on the MRI field strength, B 0. This examination is motivated by the recent interest and developments in MRI/radiotherapy hybrids where real-time imaging can be used to guide treatment beams. The ability to distinguish a tumor from background tissue is of primary importance in this field, and this work seeks to elucidate the complex relationship between the CNR and B 0 that is too often assumed to be purely linear. Methods: Experimentally based models of B 0-dependant relaxation for various tumor and normal tissues from the literature were used in conjunction with signal equations for MR sequences suitable for rapid real-time imaging to develop field-dependent predictions for CNR. These CNR models were developed for liver, lung, breast, glioma, and kidney tumors for spoiled gradient-echo, balanced steady-state free precession (bSSFP), and single-shot half-Fourier fast spin echo sequences. Results: Due to the pattern in which the relaxation properties of tissues are found to vary over B 0 field (specifically the T 1 time), there was always an improved CNR at lower fields compared to linear dependency. Further, in some tumor sites, the CNR at lower fields was found to be comparable to, or sometimes higher than those at higher fields (i.e., bSSFP CNR for glioma, kidney, and liver tumors). Conclusions: In terms of CNR, lower B 0 fields have been shown to perform as well or better than higher fields for some tumor sites due to superior T 1 contrast. In other sites this effect was less pronounced, reversing the CNR advantage. This complex relationship between CNR and B 0 reveals both low and high magnetic fields as viable options for tumor tracking in MRI/radiotherapy hybrids.

Sewage sludge can be converted into bio-material or bio-fuel by means of thermal–chemical technique. Torrefaction characteristics of municipal sewage sludge were investigated based on a thermogravimetric analysis technique in nitrogen atmosphere. The whole torrefaction process could be divided into two regions, which referred to coexistence and devolatilization. Moreover, the torrefaction kinetics of sewage sludge was evaluated based on the distributed activation energy models with differential and integral methods. There was a linear dependency between activation energy and pre-exponential factor at different conversion levels. The Gauss-Peak function was employed to depict the distribution curves of the activation energies for both methods. The distributed activation energy model developed by the integral method predicted accurately the conversion degree of the sewage sludge torrefaction, whereas the model developed by the differential method only had a good prediction for high conversion degrees.

Age–period–cohort (APC) models are designed to estimate the independent effects of age, time periods, and cohort membership. However, APC models suffer from an identification problem: There are no unique estimates of the independent effects that fit the data best because of the exact linear dependency among age, period, and cohort. Among methods proposed to address this problem, using unequal-interval widths for age, period, and cohort categories appears to break the exact linear dependency and thus solve the identification problem. However, this article shows that the identification problem remains in these models; in fact, they just implicitly impose multiple block constraints on the age, period, and cohort effects to achieve identifiability. These constraints depend on an arbitrary choice of widths for the age, period, and cohort intervals and can have nontrivial effects on the estimates. Because these assumptions are extremely difficult, if not impossible, to verify in empirical research, they are qualitatively no different from the assumptions of other constrained estimators. Therefore, the unequal-intervals approach should not be used without an explicit rationale justifying their constraints.

We investigated the wear formation during a single-asperity sliding against a rigid substrate using molecular dynamics simulations. Two distinct wear mechanisms were observed: low-load atomic wear (isolated debris atoms or clusters) and high-load plastic wear (collective debris formation from plastic flow). The atomic wear rate depends on the normal stress exponentially, in agreement with the mechanically assisted bond-rupture theory. However, the plastic wear rate exhibits linear dependency on the normal stress. It was found that the asperity-substrate adhesion reduces the critical normal stress for the atomic-to-plastic wear transition, suppressing the atomic wear mode. Finally, a wear mechanism map of atomic/plastic wear was constructed in the domain of normal stress and adhesion, which is consistent with existing simulation and experimental results. This wear map could resolve the recent controversy on whether Archard׳s linear law is applicable for low-load tip wear.

Different species of Triticum were grown during a greenhouse experiment, including T. monococcum L., T. dicoccum Schrank, T. durum Desf., T. spelta L. and T. aestivum cv. Vanek. The goal was to establish the influence of irradiance on the parameters of photosynthetic performance in relation to their ploidy. Photosynthetic rate (Pn), transpiration (E) and stomatal conductance (gs) were measured at irradiance ranging from 217–1305 μmol/m2/s. In all monitored species, saturation irradiance for photosynthesis at the level of 609 μmol/m2/s was reached. The highest average Pn was measured in the diploid T. monococcum (32.5 μmol CO2/ m2/s) while the lowest Pn occurred in the hexaploid T. spelta (22.0 μmol CO2/m 2/s). The Pn in hexaploid T. aestivum (29.6 μmol CO2/m 2/s) was comparable with the tetraploid T. durum. Similarly, E also decreased with the increase of ploidy. The highest gs was measured in T. durum (1.03 mol CO2/m 2/s) and T. aestivum (0.99 mol CO2/ m2/s). In all monitored species a close linear dependency was recorded between Pn and gs. Species with lower ploidy reach maximum values of Pn with lower gs. Hexaploid T. aestivum and tetraploid T. durum, require higher gs in order to achieve higher Pn and yet they do not reach the Pn values of species with lower ploidy.

The method of exterior forms by H. Grassmann and E. Cartan is used for solving the linear programming problem. It captures the essence of the problem in a convenient, compact form. The solution is presented by Cramer’s like rules and is reduced to computing the set of values of the objective function at the vertices of the polyhedron constraints, without any explicit calculation of the vertices themselves.

The main problem in the investigation and prediction of stress relaxation is the long time periods (not in seconds or minutes but in days or even months) of measurements for each kind of textile, especially in cases where users need to know the behaviour of the textile in prolonged time usage. Previously it was found that the rate of relaxation on the log scale can be described by two straight lines and the values of relaxation can be predicted over a long time by the rate of relaxation of the second linear dependency. The present paper shows investigations of 29.4 tex polyester yarn’s relaxation behaviour at different levels of elongation, i.e. at 3, 5, 7 and 10%. Investigations show that the place of the break-point of relaxation depends on the level of elongation – by increasing the level of elongation the time decreases till the break-point. This phenomenon is clearly visible at higher levels of elongation, while at low levels (3 and 5%) the difference is quite small. Using the data presented, it is possible to predict long-lasting relaxation without long-lasting experiments; only shorter than 1000 second tests are needed.

Groundings are among the most common and destructive maritime accidents. Sea bottom shape influences greatly what kind of damage the ship structure suffers and whether this leads to loss of water tightness. Sormunen et al. [21] presented and statistically compared rock models used in grounding damage analysis with detailed bottom shape data from two Finnish harbour fairways. The results were promising in terms of statistical fit especially for the binormal rock model, which also showed a wide range of flexibility in representing different types of sea bottom shapes. However, this measure does not explicitly tell if the model rock in grounding damage analysis results in similar damage size as real rocks cause. To test this, this paper develops a framework for studying, testing and evaluating rock models in terms of resulting grounding damage. FEM is used to analyse and compare grounding damage of rock models to the actual rock using otherwise identical grounding scenarios. Analysis is performed for four different real rocks with each rock being modelled with four different analytical rock models as well. The results show that rock models with good statistical fit did not necessarily result in similar grounding energy compared to results using the real rock. Differences in energy are caused especially by the rougher surface of the real rocks. For the similarity in rock area and the damaged ship structure element volume the results are much better, especially for the binormal model. As such another criteria for evaluating rock models for grounding damage analysis is needed. The results show that the damaged material volume is strongly linearly dependent on the rock area- and volume metrics. A similar linear dependency exists between the damaged volume and the energy dissipated in grounding. Knowledge of these relationships can be used towards estimating grounding damage of ships in future investigations, but rock surface unevenness should be evaluated as well.