Study on tracheal collapsibility, compliance, and stress by considering nonlinear mechanical property of cartilage

Tracheal cartilage has been widely regarded as a linear elastic material either in experimental studies or in analytic and numerical models. However, it has been recently demonstrated that, like other fiber-oriented biological tissues, tracheal cartilage is a nonlinear material, which displays higher strength in compression than in extension. Considering the nonlinearity requires a more complex theoretical frame work and costs more to simulate. This study aims to quantify the deviation due to the simplified treatment of the tracheal cartilage as a linear material. It also evaluates the improved accuracy gained by considering the nonlinearity. Pig tracheal rings were used to exam the mechanical properties of cartilage and muscular membrane. By taking into account the asymmetric shape of tracheal cartilage, the collapse behavior of complete rings was simulated, and the compliance of airway and stress in the muscular membrane were discussed. The results obtained were compared with those assuming linear mechanical properties. The following results were found: (1) Models based on both types of material properties give a small difference in representing collapse behavior; (2) regarding compliance, the relative difference is big, ranging from 10 to 40% under negative pressure conditions; and (3) the difference in determining stress in the muscular membrane is small too: <5%. In conclusion, treating tracheal cartilage as a linear material will not cause big deviations in representing the collapse behavior, and mechanical stress in the muscular part, but it will induce a big deviation in predicting the compliance, particularly when the transmural pressure is lower than -0.5 kPa. The results obtained in this study may be useful in both understanding the collapse behavior of trachea and in evaluating the error induced by the simplification of treating the tracheal cartilage as a linear elastic material.

Energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements

This work deals with the formulation and implementation of an energy-momentum conserving algorithm for conducting the nonlinear transient analysis of structures, within the framework of stress-based hybrid elements. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements within the static framework. We show that this advantage carries over to the transient case, so that not only are the solutions obtained more accurate, but they are obtained in fewer iterations. We demonstrate the efficacy of the algorithm on a wide range of problems such as ones involving dynamic buckling, complicated three-dimensional motions, et cetera.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

Nonlinear mechanical property of tracheal cartilage: A theoretical and experimental study

Background: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. Method: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. Result: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03 N and from -0.03 to -0.04 N, the deformation ratios were 11.03±2.18% and 7.27±1.59%, respectively. Both were much smaller than the deformation ratios (20.01±4.49%) under tension forces of 0.02 to 0.01 N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Studies in Nonlinear Optical Materials: Structure of 3-Menthyl 2-[Bis(dimethylarnino)methylene]-3-oxobutyrate Hemihydrate

C 19Ha4N203.~xH 2 O, Mr= 347.5, monoclinic, C2, a = 15.473 (3), b = 6.963 (2), c = 20.708 (4) ]1, //=108.2(2) ° , V=2119(2)A 3, Z=4, Ox= 1.089 Mg m -3, ,~(Cu Ktx) = 1.5418 ]1, p = 0.523 mm -~, F(000) = 760.0, T= 293 K, R = 0.068 for 1967 unique reflections. The C=C bond length is 1-447 (6)]1, significantly longer than in ethylene, 1.336 (2)]1. The crystal structure is stabilized by O-H...O hydrogen bonding. Explanation for the observed low second-harmonic-generation efficiency (0.5 times that of urea) is provided.

Studies in Nonlinear Optical Materials: Structure of Methyl 2-(4-Ethyl-5-methyl- 2-thioxo-2,3-dihydro-l,3-thiazol- 3-yl) propionate

CIoH15NO282, Mr=245"0, orthorhombic, P21212 ~, a = 6.639 (2), b = 8.205 (2), c = 22.528(6)A, V= I227.2(6)A 3, z=4, Dm= 1.315, Dx= 1.326gem -3, MoKa, 2=0.7107A, 12= 3.63 cm -1, F(000) = 520, T= 293 K, R = 0.037 for 1115 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is only 1/10th of the urea standard. The observed low second-order nonlinear response may be attributed to the unfavourable packing of the molecules in the crystal lattice.

Use of 45° pulse pair as a filter for pure-phase two-dimensional NMR spectroscopy

Conventionally two-dimensional NMR spectra are recorded in the absolute-intensity mode (1-4). It has recently been demonstrated that absorption-mode 2D spectra have much higher resolution and are the preferred mode of presentation, especially for 2D spectra of biomolecules (5-7). Indeed, any experimental scheme which yields phasemixed lineshapes is subject to modification to yield pure-phase spectra, even at the expense of intensity and anomalous multiplet structure (8-10). For this purpose two types of filters are already known: the z filter (9, 20) and the purging pulse (8, 10). In this note, we propose a 45” pulse pair as a filter for obtaining pure-phase 2D spectra, mainly for experiments in which the above filters do not yield pure-phase spectra.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Nonlinear analysis for the pre- and post-yield behaviour of a composite structure with the refined plastic hinge approach

The computational technique of the full ranges of the second-order inelastic behaviour evaluation of steel-concrete composite structure is not always sought forgivingly, and therefore it hinders the development and application of the performance-based design approach for the composite structure. To this end, this paper addresses of the advanced computational technique of the higher-order element with the refined plastic hinges to capture the all-ranges behaviour of an entire steel-concrete composite structure. Moreover, this paper presents the efficient and economical cross-section analysis to evaluate the element section capacity of the non-uniform and arbitrary composite section subjected to the axial and bending interaction. Based on the same single algorithm, it can accurately and effectively evaluate nearly continuous interaction capacity curve from decompression to pure bending technically, which is the important capacity range but highly nonlinear. Hence, this cross-section analysis provides the simple but unique algorithm for the design approach. In summary, the present nonlinear computational technique can simulate both material and geometric nonlinearities of the composite structure in the accurate, efficient and reliable fashion, including partial shear connection and gradual yielding at pre-yield stage, plasticity and strain-hardening effect due to axial and bending interaction at post-yield stage, loading redistribution, second-order P-δ and P-Δ effect, and also the stiffness and strength deterioration. And because of its reliable and accurate behavioural evaluation, the present technique can be extended for the design of the high-strength composite structure and potentially for the fibre-reinforced concrete structure.

A Unique Filter-Preserver Device for Digital Photonic Circuits

We discuss micro ring resonator based optical logic gates using Kerr-type nonlinearity. Resonant wavelength selectivity is one key factor in achieving the desired gate. Based on basic gates like AND gate, OR gate etc. We proceed to propose a 3-bit binary adder circuit.Due to the presence of more than a single wavelength, the system gets complicated as we increase the number of components in the circuit. Hence it has been observed that for efficient designing and functioning of digital circuits in optical domain, we need a device which can give single wavelength output, filtering out all other wavelengths and at the same time preserve the digital characteristics of the output. We propose such filter-preserver device based on micro ring resonator.

Nonlinear I-V characteristics of senmiconducting paints

The oxide-based high resistivity semiconducting Paints can be used on high voltage insulators for improved performance. They were found to exhibit nonlinear I-V characteristics which are reported here. The paints exhibited power law relationship and a sharp transition in merhanism of conduction at a critical voltage.

3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.