* Correspondence: ahmed.koubaa@uqat.ca; Tel.: +01-819-761-0971 (ext. 2579)
† This manuscript is part **of** an M.S. thesis by the first author, available online at depositum.uqat.ca .
Received: 30 May 2019; Accepted: 4 July 2019; Published: 9 July 2019 Abstract: Currently, ultrasonic measurement is a widely used nondestructive approach to determine wood elastic properties, including the dynamic **modulus** **of** **elasticity** (DMOE). DMOE is determined based on wood density and ultrasonic wave velocity measurement. The use **of** wood average density to estimate DMOE introduces significant imprecision: Density varies due to intra-tree and intra-ring differences and differing silvicultural treatments. To ensure accurate DMOE assessment, we developed a prototype device to measure ultrasonic wave velocity with the same resolution as that provided by the X-ray densitometer for measuring wood density. A nondestructive method based on X-ray densitometry and the developed prototype was applied to determine radial and intra-ring wood DMOE profiles. This method provides accurate information on wood mechanical properties and their sources **of** variation. High-order polynomials were used to model intra-ring wood density and DMOE profiles in black spruce and jack pine wood. The transition from earlywood to latewood was defined as the inflection point. High and highly significant correlations were obtained between predicted and measured wood density and DMOE. An examination **of** the correlations between wood radial growth, density, and DMOE revealed close correlations between density and DMOE in rings, earlywood, and latewood

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thus the coefficient **of** variation (6.95 and 2.67%) is obviously lower than in the exper- imental results from (around 15% regardless **of** the group).
The experimental ratio between the dynamic MOE **of** juvenile and mature wood is 0.876, which is higher than the model prediction (0.785). However, the results **of** Rahayu et al. (2014) present a higher coefficient **of** variation (Table 1) . The study’s ratio is included between 0.69 and 1.06 by considering both standard deviations **of** ju- venile and mature **modulus** **of** **elasticity**. Indeed, uncertainty **of** a ratio can be calculated from the standard deviation **of** each part **of** this ratio. Therefore the results obtained with the model are close or similar to those from Rahayu et al. (2014). However, several reasons could have induced different ratios. From the experimental point **of** view, there exist difficulties in distinguishing juvenile from mature wood in Rahayu et al. (2014). Indeed, groups were made by visual observation **of** false heartwood but false heartwood does not necessarily correspond exactly to juvenile wood. Furthermore, a part **of** the studied logs was quite young, with a first quartile equal to 13.25 years, which leads to a minor number **of** mature annual growth rings to obtain a reliable long term evolution **of** mature wood properties. From the modelling point **of** view, there is a lack **of** exper- imental input data for mature wood in the literature (Thibaut et al. 2015), entailing an assumption **of** steady parameters for extra dataset domain for raw material properties. By doing so, the MOE **of** mature wood is bounded in the model, and the dispersion **of** LVL composed **of** mature wood is very low in comparison with experimental measure- ments. Thus the MOE can be underestimated, especially for mature wood, leading to the higher ratio between the juvenile and mature wood MOE observed in the model.

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The **modulus** **of** **elasticity** **of** leda clay from field measurements
Bozozuk, M.
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4. Conclusions
Measuring the phase change along a draw-away line and conducting a regression analysis to determine the real part **of** the wavenumber is a relatively simple task. Wavenumber measurements along draw-away lines parallel and perpendicular to the joists confirmed the highly orthotropic nature **of** a wood joist floor. Measurements suggest that the degree **of** orthotropy in the direction parallel to the joists could be partially determined by the complex interaction **of** the OSB floor sheathing between the joists. It is suggested that below the cut-on frequency **of** the first cross mode, the joists significantly affect the stiffness **of** the OSB floor sheathing parallel to the joists. Above the frequency **of** the first cross mode, the effect **of** the joists is significantly reduced and in the limit, as the bending wavelength becomes much smaller than the joist spacing, the wavenumber (and bending stiffness) approaches that **of** the OSB floor sheathing in isolation. Wavenumbers in the direction parallel to the joists also approached those measured on OSB floor sheathing in isolation.

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tr(Wc j c H j ) = |v j | 2 j = 1, ..., J, (13c)
W < 0. (13d)
V. C ONVEX M ODIFIED L INEARLY C ONSTRAINED CMA
The CM cost function is insensitive to the phase **of** the signal carrier. Therefore, in the presence **of** an unknown phase rotation the resulting estimated signal will also be rotated. A phase-sensitive modification **of** the CM cost function, referred to as the MCM, was introduced in [6], aimed at enabling improved performance for high order QAM and carrier phase synchronization. To introduce the MCM cost function, let w R , w I and y R (t), y I (t) denote, respectively, the real and

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Introduction
The Urban Roads group **of** the National Research Council Canada has recently developed a new characterization scheme for determining the mechanistic properties **of** unbound materials (Khogali and Hussein, 2004). The established technique, named the M r –PD test, goes beyond the conventional method **of** determining the resilient **modulus** (M r ) by concurrently measuring the percentage permanent deformation (%PD) that the material accumulates under dynamic loading. The two parameters obtained from the test define the full material response; thus making it an effective method for assessing the material’s potential performance under prevailing in-situ conditions. Obtaining the two parameters in the laboratory for a wide range **of** physical and loading conditions is an expensive and time-consuming undertaking. This paper presents an approach that circumvents the need for extensive M r –PD testing by combining the use **of** limited laboratory-generated data with analytical modeling to produce adequate size databases.

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Preface
The thesis is part **of** a program that aims to study the holomorphic classica- tion **of** generic unfoldings **of** the simplest codimension-one singularities **of** ana- lytic dynamical systems, the latter being given by germs **of** diffeomorphisms (in which case we study classication under conjugacy) or germs **of** vector elds (in which case we can study either classication under orbital equivalence or under conjugacy). The moduli space for these singularities has been described by J. Ecalle, S. M. Voronin (cf. [14],[51]) and J. Martinet-J. P. Ramis (cf. [35],[36]). In spite **of** the “simple” shape **of** these germs, except for the case **of** the node **of** a planar vector eld, the moduli space is a huge functional space, while, on the other hand, the formal invariants are in nite number. This means that there is an innite number **of** analytic obstructions for the analytic equivalence **of** two germs, that cannot be seen at the formal level. The former idea **of** V. I. Arnold et al. is that the **modulus** associated with the singularity can be explained by rst, complexifying the underlying space and then, by unfolding the singularity. Thus, the singularity **of** the dynamical system comes from the coallescence in a generic unfolding **of** a nite number **of** hyperbolic singularities or special hyperbolic “ob- jects” (like a periodic orbit or a limit cycle). Each hyperbolic object has its own geometric local model, and the **modulus** measures the mismatch **of** these local

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Competing Interests: The authors have declared that no competing interests exist. * E-mail: npatel@bidmc.harvard.edu
Introduction
Macrophages, despite arising from a common monocyte- granulocyte lineage, perform a myriad **of** functions such as host defense from infection, control **of** inflammation, and repair **of** injury [1,2,3] in order to preserve organ homeostasis. This is well demonstrated in the lungs where alveolar macrophages are the first line **of** host defense and serve as critical activators **of** inflammation promoting recruitment **of** neutrophils and other immune cells during the early stages **of** pneumonia [4]. Later in the course **of** pneumonia, alveolar macrophages are critical for controlling inflammation, limiting collateral damage, and promot- ing resolution through phagocytosis **of** bacteria, apoptotic host cells, and debris [5,6]. While lower respiratory tract infections comprise the single largest burden **of** disease worldwide as assessed by disability adjusted life years (DALYS) [7], there remains limited understanding **of** how dynamic regulation **of** macrophage function is achieved to preserve lung function. Regulation **of** macrophage function is presently understood mainly in the context **of** ligation events and downstream signaling [2,3] and attempts at describing macrophage phenotype have largely focused on changes in gene expression [8]. In the lungs, where mechanics play a critical role in determining organ function [9], pneumonia is typically associated with large increases in local tissue rigidity and decreases in tissue stretch [10,11]. It is also well recognized that biologic modulators such as bacterial pathogen associated molecular patterns (PAMPs) or cytokines increase both lung tissue rigidity [12,13], and cell

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Keywords: Nonlinearly elastic plates, derivation of two-dimensional models, nonexistence for membranes under compression, Ogden materials, incompressible materials, formal asymptotic exp[r]

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The models presented in Table 1 have several limitations. The major drawback **of** these equations is associated with the use **of** classical statistical principles to extrapolate parameters outside the range **of** the tests performed. The majority **of** test results were generated within a temperature range **of** 5 to 40 o C. This resulted in unrealistically large and small predictive moduli for very cold and very hot conditions outside this range. Fonseca and Witczak observed that the majority **of** these predictive equations were based on the original bitumen properties, with the test temperature being the most important variable in the system. However, these predictive equations do not account for the hardening effects on binders, and consequently the AC properties associated with long-term aging.

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4. Conclusions
We have obtained a new expression for the elastic shear **modulus** **of** a colloidal suspension modeled as a solid. This expression allows to estimate the elastic **modulus** **of** a yield stress suspension submitted to a load smaller than the yield stress. This result was obtained in the framework **of** an homogenization approach to the behavior **of** a colloidal suspension considered as a discrete solid medium. Even if this approach relies on assumptions rather different from those classically performed to obtain estimates for the overall properties **of** suspensions in the framework **of** statistical mechanics, it is worth noting that classical results can also be recovered. Thus, we have shown that our estimate coincides with the classical high-frequency **modulus** estimate when the actual configuration is taken as the reference. From our point **of** view, this result was recovered by modeling the suspension as a “liquid”, ie a suspension without a yield stress. In this situation, it is not possible to define an “undeformed” configuration and the actual configuration is taken as the reference. To our opinion, this similarity is a strong indication that both approaches are consistent one to the other.

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The strain rate and temperature dependence **of** Young's **modulus** **of** ice Traetteberg, A.; Gold, L. W.; Frederking, R. M. W.
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4.2. Limitations and opportunities
Aspects **of** the specific method used in this study limit the inter- pretation **of** the results. These limitations pertain to the structure **of** printed parenchyma models and stem from a variety **of** sources. Limitations associated primarily with imaging and image process- ing will be discussed first. The relative density range **of** the test specimens is limited and their absolute values exceed 0.3. It was initially planned to test lower densities, but the images, and, to a greater degree the generated STL files, had cell wall connectivity issues that required the images to be dilated to remove the holes at nodes **of** the cell walls. It should also be noted that the binary operation did not result in all cell walls being completely con- nected. There were rare instances in the cell wall where the grey value was considerably lower and thresholded as background. These instances were not corrected, as they may correspond to physical regions **of** the actual cell wall with much lower stiffness and poorer load transfer capability. In higher density structures, some **of** these areas may become solid cell wall, resulting in stiff- ness increases due to increased connectivity and higher density.

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ABSTRACT: The process **of** pavement design requires the provision **of** material properties. For mechanistic–empirical design methods, the resilient **modulus** represents the most suitable alternative for describing the behavior **of** aggregate materials commonly used in sub-base and base layers. However, the adoption **of** the resilient **modulus** has been slow due to the complicated nature **of** the laboratory test used to obtain the parameter and its cost. Attempts to correlate the resilient **modulus** to the widely used California Bearing Ratio and other empirical parameters in the past fall short **of** providing reasonably accurate estimates **of** the parameter. With the renewed interest in using the resilient **modulus** as advocated by the AASHTO 2002 Guide, a quick and inexpensive solution to providing accurate estimates **of** this parameter is needed. This paper presents the artificial neural network (ANN) technique as a promising method that can help designers have a good first-step estimation **of** the resilient **modulus** based on data accumulated over the years. The study highlights the use **of** the ANN technique, which utilizes simple parameters as input to predict the resilient **modulus** **of** unbound granular materials. Results **of** ANN simulations confirm the potential **of** the technique to predict the resilient **modulus** **of** compacted samples tested at various compaction densities, states **of** stress and moisture contents. Such a tool represents an attractive alternative to laboratory testing for small jurisdictions with limited budgets and personnel.

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looked through the lens **of** polymer theories that rest too heavily on the Gaussianity **of** the chains.
To conclude our analysis, we also apply our theoretical expressions to two sets **of** data, which have been recently published. Both experiments have been carried out in the group **of** Gong. 21 , 30 The ﬁrst system is a tetra-PEG hydrogel composed **of** monodisperse long chains that can be greatly swollen by using a combined approach **of** adding a molecular stent and applying a PEG dehydration method. 21 Because the system is monodisperse and the chains are quite long, we expect the theoretical expressions derived here to work well. Indeed, as shown in Figure 7 d, the resulting Young ’s **modulus** is a nonmonotonic function **of** the swelling ratio Q, de ﬁned as the ratio between the volume at which the measurements are performed and the volume at which the sample was synthesized. The experimental data can be ﬁtted with both the L-FJC and WLC expressions (see Appendix A ) because both models reproduce the data with high accuracy when ﬁtted with the two free parameters introduced above (R 0 and ⟨n⟩). However, better results are obtained with the WLC model, which ﬁts well when ⟨n⟩ is ﬁxed to its experimentally estimated value, yielding a value R 0 = 7.2 nm, which is very close to the independently estimated value **of** 8.1 nm, 21 in agreement with what reported in Hoshino et al. 21

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determine the velocity **of** the fluid v (see Figure 1).
One specific example **of** the above mentioned model is a 3D tube with elastic walls through which a fluid is flowing. From the physical point **of** view, this is a very important model with a lot **of** applications in mathematical biology, more precisely, the study **of** arterial diseases (the tube represents the artery, the elastic body is the wall **of** the artery and the fluid is the blood).

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