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NASA NTRS2016

Organic Analysis in the Miller Range 090657 CR2 Chondrite: Part 2 Amino Acid Analyses

Primitive carbonaceous chondrites contain a wide variety of organic material, ranging from soluble discrete molecules to insoluble, unstructured kerogen-like components, as well as structured nano-globules of macromolecular carbon. The relationship between the soluble organic molecules, macromolecular organic material, and host minerals are poorly understood. Due to the differences in extractability of soluble and insoluble organic materials, the analysis methods for each differ and are often performed independently. The combination of soluble and insoluble analyses, when performed concurrently, can provide a wider understanding of spatial distribution, and elemental, structural and isotopic composition of organic material in primitive meteorites. Using macroscale extraction and analysis techniques in combination with in situ microscale observation, we have been studying both insoluble and soluble organic material in the primitive CR2 chondrite Miller Range (MIL) 090657. In accompanying abstracts (Cao et al. and Messenger et al.) we discuss insoluble organic material in the samples. By performing the consortium studies, we aim to improve our understanding of the relationship between the meteorite minerals and the soluble and insoluble organic phases and to delineate which species formed within the meteorite and those that formed in nebular or presolar environments. In this abstract, we present the results of amino acid analyses of MIL 090657 by ultra performance liquid chromatography with fluorescence detection and quadrupole-time of flight mass spectrometry. Amino acids are of interest because they are essential to life on Earth, and because they are present in sufficient structural, enantiomeric and isotopic diversity to allow insights into early solar system chemical processes. Furthermore, these are among the most isotopically anomalous species, yet at least some fraction are thought to have formed by aqueously-mediated processes during parent body alteration.

Burton, A. S.↗
DOE OSTI2022

Numerical Study on the Effect of Methane Doping in Hydrogen-Air Rotating Detonation Engines for Various Temperatures and Pressures

Rotating detonation engines (RDEs) have gained attention as a promising technology for future aviation engines. However, the numerical studies of these systems pose severe challenges due to the broad range of spatial and temporal scales. In this study, we use an adaptive mesh refinement based compressible, reactive solver PeleC to resolve the broad range of scales and accurately capture shock and detonation waves using high-resolution numerical schemes. Multi- species transport along with compressible Navier-Stokes equations are solved in the model along with a finite-rate based chemistry model. Embedded boundary method is used to model the complex geometry consisting of discrete fuel nozzles and the combustion chamber. The fuel consisting predominantly of hydrogen is doped with varying levels of methane while air is used as the oxidizer. For a specified total pressure and temperature, the number of stable detonation waves is found to decrease with increasing methane concentration in the fuel mixture. Additionally, no stable detonation solutions are observed for methane composition higher than 20% by volume for the range of operating conditions studied (300-900K, 10 Atm). The increased presence of high temperature zones is also indicative of higher thermal NOx emissions at low methane concentrations. The effect of fuel-air mixture composition and temperature on the detonability, detonation wave structure, mode transitions and their stability are analyzed in this study in addition to their implication on NOx emission.

automatic mesh refinement↗
NASA NTRS2001

Modelling of Trapped Radiation Near Jupiter

Energetic (62 to approx. 130 MeV) proton fluxes measured with the Galileo Probe inside Jupiter's main ring (radii 122,500 to 128,940 km) show a modest increase as Jupiter is approached. Solutions of a reduced (1-d) equatorial diffusion equation with-constant losses described by a lifetime tau match those data for tau greater than or equal to 10(exp 9) s for diffusion coefficient D(sub LL) = 10(exp -9) L(exp 4)/s, 10(exp -9) L(exp -3)/s, or 10(exp -10) L(exp 4)/s (this particle population may be undergoing nearly loss-free inward radial diffusion). Tau would increase as Jupiter is approached if its value were determined by pitch angle scattering due to EM wave-particle interactions. if the absolute amplitudes of the waves' magnetic fluctuations did not vary with radial distance. Exploration of numerical solutions of the diffusive transport equation for Jupiter's magnetospheric ions at die planetary ring and closer to Jupiter has been done. Explicit range-energy relationships for energy loss in ring matter (SiO2), modeled as a continuous disk, are incorporated. A spatial resolution of approx. 1000 km in the radial direction is used in the vicinity of the main ring; off-equatorial ion fluxes have been included (assuming the atmosphere is a perfect absorber). For protons the maximum effect of energy loss in the microscopic size range of ring particles is expected at energies approx. 0.1 Mev. Presumably there could be sufficiently large, unobserved bodies within the ring that would have to be modeled as discrete objects, as planetary satellites would be. Within limitations of the model and computational resources it's planned to characterize solutions for transport of magnetospheric ions past the planetary ring; the procedures that are used are fairly well known and may be applied generally to the simpler magnetospheric models.

Mihalov, John D.↗
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
NASA NTRS2011

High Frequency Acoustic Response Characterization and Analysis of the Deep Throttling Common Extensible Cryogenic Engine

The Common Extensive Cryogenic Engine program demonstrated the operation of a deep throttling engine design. The program, spanning five years from August 2005 to July 2010, funded testing through four separate engine demonstration test series. Along with successful completion of multiple objectives, a discrete response of approximately 4000 Hz was discovered and explored throughout the program. The typical low-amplitude acoustic response was evident in the chamber measurement through almost every operating condition; however, at certain off-nominal operating conditions, the response became discrete with higher amplitude. This paper summarizes the data reduction, characterization, and analysis of the 4,000 Hz response for the entire program duration, using the large amount of data collected. Upon first encountering the response, new objectives and instrumentation were incorporated in future test series to specifically collect 4,000 Hz data. The 4,000 Hz response was identified as being related to the first tangential acoustic mode by means of frequency estimation and spatial decomposition. The latter approach showed that the effective node line of the mode was aligned with the manifold propellant inlets with standing waves and quasi-standing waves present at various times. Contour maps that contain instantaneous frequency and amplitude trackings of the response were generated as a significant improvement to historical manual approaches of data reduction presentation. Signal analysis and dynamic data reduction also uncovered several other features of the response including a stable limit cycle, the progressive engagement of subsequent harmonics, the U-shaped time history, an intermittent response near the test-based neutral stability region, other acoustic modes, and indications of modulation with a separate subsynchronous response. Although no engine damage related to the acoustic mode was noted, the peak-to-peak fluctuating pressure amplitude achieved 12.1% of the mean chamber pressure at its highest. The identification of this response in terms of an instability is also discussed.

Casiano, M. J.↗
DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Analysis of soot formation from aviation fuels in laminar counterflow flames

Combustion emissions from aviation contribute to the formation of condensation trail (contrail) that can lead to the formation of anthropogenic cirrus clouds. Ice particles that form contrails are observed to have a linear correlation with soot particle number density. Synthetic aviation fuels (SAFs) offer a promising route to mitigate the production of soot particles while also increasing energy security. Although studies have focused on combustion and spray behavior, the detailed investigation of soot formation processes for different jet fuels and their impact on models for computational fluid dynamics (CFD) applications is not well understood. Moreover, experimental measurements of soot for canonical flames using Synthetic aviation fuels (SAF) for model validation remain scarce. To address this, we use employed the Lawrence Livermore National Laboratory (LLNL) detailed soot model based on the discrete sectional method. Additionally, we develop two reduced chemical mechanisms for Jet-A and Alcohol-to-Jet (C1) that are suitable for turbulent flame simulations and couple them with the Hybrid Method of Moments (HMOM). The detailed and reduced model frameworks are validated against experimental measurements of soot volume fraction (ƒ ν ) from a counterflow burner experiment previously reported in the literature. Given the good agreement between modeling results and experimental measurements for the (1) spatial distribution of ƒ ν and (2) the non-linear variation of peak ƒ ν with strain rate, we further investigate the modeled sub-processes (nucleation, condensation, surface growth, and oxidation) using the LLNL model to analyze the assumptions in the reduced model framework. Furthermore, the results indicate a significant contribution from resonant radicals to the surface growth of soot particles, which are not accounted for in the current implementation of HMOM and could help reconcile soot predictions by the reduced model with observations.

Counterflow↗
DOE OSTI2024

Uncertainty-aware Continuous Implicit Neural Representations for Remote Sensing Object Counting

Many existing object counting methods rely on density map estimation (DME) of the discrete grid representation by decoding extracted image semantic features from designed convolutional neural networks (CNNs). Relying on discrete density maps not only leads to information loss dependent on the original image resolution, but also has a scalability issue when analyzing high-resolution images with cubically increasing memory complexity. Furthermore, none of the existing methods can offer reliable uncertainty quantification (UQ) for the derived count estimates. To overcome these limitations, we design UNcertainty-aware, hypernetwork-based Implicit neural representations for Counting (UNIC) to assign probabilities and the corresponding counting confidence over continuous spatial coordinates. We derive a sampling-based Bayesian counting loss function and develop the corresponding model training algorithm. UNIC outperforms existing methods on the Remote Sensing Object Counting (RSOC) dataset with reliable UQ and improved interpretability of the derived count estimates. Our code is available at https://github.com/SiyuanXu-tamu/UNIC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Towards high-precision parton distributions from lattice QCD via distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Mapping the Moon in Soft x Rays: Promises and Challenges

Recent ROSAT images reported by Schmitt et el. show that the sunlit part of the Moon is a significant source of very soft x rays. Stimulated by these observations, Edwards et al. have made an analysis of the response of the Moon to the solar soft x ray and EUV spectrum. They argue that much of the observed emission is in the form of discrete fluorescence lines in the energy range 25 to 100 eV, and that these lines are generally much stronger than the adjacent directly scattered solar background. On this basis they suggest that soft x ray fluorescence can be used to remotely obtain high-precision elemental maps of the lunar surface. Edwards et al. have continued to develop this idea and have suggested a system using soft x ray telescopes in lunar orbit, which could also obtain very good spatial resolution. This combination could be extremely valuable in furthering our understanding of lunar chemistry and potential resource distributions. High spatial resolution combined with the thin surface layer from which these soft x rays arise suggests the exciting possibility that x ray telescopes could map lunar volcanic volatiles from orbit.

Housley, R. M.↗
NASA NTRS1995

CNR LARA project, Italy: Airborne laboratory for environmental research

The increasing interest for the environmental problems and the study of the impact on the environment due to antropic activity produced an enhancement of remote sensing applications. The Italian National Research Council (CNR) established a new laboratory for airborne hyperspectral imaging, the LARA Project (Laboratorio Aero per Ricerche Ambientali - Airborne Laboratory for Environmental Research), equipping its airborne laboratory, a CASA-212, mainly with the Daedalus AA5000 MIVIS (Multispectral Infrared and Visible Imaging Spectrometer) instrument. MIVIS's channels, spectral bandwidths, and locations are chosen to meet the needs of scientific research for advanced applications of remote sensing data. MIVIS can make significant contributions to solving problems in many diverse areas such as geologic exploration, land use studies, mineralogy, agricultural crop studies, energy loss analysis, pollution assessment, volcanology, forest fire management and others. The broad spectral range and the many discrete narrow channels of MIVIS provide a fine quantization of spectral information that permits accurate definition of absorption features from a variety of materials, allowing the extraction of chemical and physical information of our environment. The availability of such a hyperspectral imager, that will operate mainly in the Mediterranean area, at the present represents a unique opportunity for those who are involved in environmental studies and land-management to collect systematically large-scale and high spectral-spatial resolution data of this part of the world. Nevertheless, MIVIS deployments will touch other parts of the world, where a major interest from the international scientific community is present.

Bianchi, R.↗
NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗
NASA NTRS1990

Empirical relationships between gas abundances and UV selective extinction

Several studies of gas-phase abundances in lines of sight through the outer edges of dense clouds are summarized. These lines of sight have 0.4 less than E(B-V) less than 1.1 and have inferred spatial densities of a few hundred cm(-3). The primary thrust of these studies has been to compare gaseous abundances in interstellar clouds that have various types of peculiar selective extinction. To date, the most notable result has been an empirical relationship between the CN/Fe I abundance ratio and the depth of the 2200 A extinction bump. It is not clear at the present time, however, whether these two parameters are linearly correlated or the data are organized into two discrete ensembles. Based on 19 samples and assuming the clouds form discrete ensembles, lines of sight that have a CN/Fe I abundance ratio greater than 0.3 (dex) appear to have a shallow 2.57 plus or minus 0.55 bump compared to 3.60 plus or minus 0.36 for other dense clouds and compared to the 3.6 Seaton (1979) average. The difference in the strength of the extinction bump between these two ensembles is 1.03 plus or minus 0.23. Although a high-resolution IUE survey of dense clouds is far from complete, the few lines of sight with shallow extinction bumps all show preferential depletion of certain elements, while those lines of sight with normal 2200 A bumps do not. Ca II, Cr II, and Mn II appear to exhibit the strongest preferential depletion compared to S II, P II, and Mg II. Fe II and Si II depletions also appear to be enhanced somewhat in the shallow-bump lines of sight. It should be noted that Copernicus data suggest all elements, including the so-called nondepletors, deplete in diffuse clouds (Snow and Jenkins 1980, Joseph 1988). Those lines of sight through dense clouds that have normal 2200 A extinction bumps appear to be extensions of the depletions found in the diffuse interstellar medium. That is, the overall level of depletion is enhanced, but the element-to-element abundances are similar to those in diffuse clouds. In a separate study, the abundances of neutral atoms were studied in a dense cloud having a shallow 2200 A bump and in one with a normal strength bump.

Joseph, Charles L.↗
NASA NTRS1992

Spectral analysis for automated exploration and sample acquisition

Future space exploration missions will rely heavily on the use of complex instrument data for determining the geologic, chemical, and elemental character of planetary surfaces. One important instrument is the imaging spectrometer, which collects complete images in multiple discrete wavelengths in the visible and infrared regions of the spectrum. Extensive computational effort is required to extract information from such high-dimensional data. A hierarchical classification scheme allows multispectral data to be analyzed for purposes of mineral classification while limiting the overall computational requirements. The hierarchical classifier exploits the tunability of a new type of imaging spectrometer which is based on an acousto-optic tunable filter. This spectrometer collects a complete image in each wavelength passband without spatial scanning. It may be programmed to scan through a range of wavelengths or to collect only specific bands for data analysis. Spectral classification activities employ artificial neural networks, trained to recognize a number of mineral classes. Analysis of the trained networks has proven useful in determining which subsets of spectral bands should be employed at each step of the hierarchical classifier. The network classifiers are capable of recognizing all mineral types which were included in the training set. In addition, the major components of many mineral mixtures can also be recognized. This capability may prove useful for a system designed to evaluate data in a strange environment where details of the mineral composition are not known in advance.

Eberlein, Susan↗
NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
DOE OSTI2024

Characterizing the microstructures of mammalian enamel by synchrotron phase contrast microCT

The enamel of mammalian teeth is a highly mineralized tissue that must endure a lifetime of cyclic contact and is inspiring the development of next-generation engineering materials. Attempts to implement enamel-inspired structures in synthetic materials have had limited success, largely due to the absence of a detailed understanding of its microstructure. Here, the present work used synchrotron phase-contrast microCT imaging to evaluate the three-dimensional microstructure of enamel from four mammals including Lion, Gray Wolf, Snow Leopard, and Black Bear. Quantitative results of image analysis revealed that the decussation pattern of enamel consists of discrete diazone (D) and parazone (P) bands of rods organized with stacking arrangement of D+/P/D-/P in all mammals evaluated; the D+ and D- refer to distinct diazone bands with juxtaposed rod orientations from the reference plane. Furthermore, the rod orientations in the bands can be described in terms of two principal angles, defined here as the pitch and yaw. While the pitch angle increases from the outer enamel to a maximum (up to ≈ 40°) near the dentin enamel junction, minimal spatial variations are observed in yaw across the enamel thickness. There are clear differences in the decussation parameters of enamel across species that are interpreted here with respect to the structural demands placed on their teeth. The rod pitch and band width of enamel are identified as important design parameters and appear to be correlated with the bite force quotient of the four mammals evaluated.

36 MATERIALS SCIENCE↗