Selected Mathematical Models Describing Flow in Gas Pipelines

The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of load and supply will help us find out the value of pressure or flow rate at selected points or along selected sections of the network. Transient gas flow may be described by a set of simple or partial differential equations classified as hyperbolic or parabolic. Derivation of the mathematical model of transient gas flow involves certain simplifications, of which one-dimensional flow is most important. It is very important to determine the conditions of pipeline/transmission network operation in which the hyperbolic model and the parabolic model, respectively, should be used. Parabolic models can be solved numerically in a much simpler way and can be used to design simulation programs which allow us to calculate the network of any structure and any number of non-pipe elements. In some conditions, however, they describe the changes occurring in the network less accurately than hyperbolic models do. The need for analysis, control, and optimization of gas flows in high-pressure gas pipelines with complex structure increases significantly. Very often, the time allowed for analysis and making operational decisions is limited. Therefore, efficient models of unsteady gas flows and high-speed algorithms are essential.

Effects of photosynthetic models on the calculation results of photosynthetic response parameters in young Larix principis-rupprechtii Mayr. plantation

Accurately predicting the crown photosynthesis of trees is necessary for better understanding the C circle in terrestrial ecosystem. However, modeling crown for individual tree is still challenging with the complex crown structure and changeable environmental conditions. This study was conducted to explore model in modeling the photosynthesis light response curve of the tree crown of young Larix principis-rupprechtii Mayr. Plantation. The rectangular hyperbolic model (RHM), non-rectangular hyperbolic model (NRHM), exponential model (EM) and modified rectangular hyperbolic model (MRHM) were used to model the photosynthetic light response curves. The fitting accuracy of these models was tested by comparing determinants coefficients (R2), mean square errors (MSE) and Akaike information criterion (AIC). The results showed that the mean value of R2 of MRHM (R2 = 0.9687) was the highest, whereas MSE value (MSE = 0.0748) and AIC value (AIC = -39.21) were the lowest. The order of fitting accuracy of the four models for Pn-PAR response curve was as follows: MRHM > EM > NRHM > RHM. In addition, the light saturation point (LSP) obtained by MRHM was slightly lower than the observed values, whereas the maximum net photosynthetic rates (Pmax) modeled by the four models were close to the measured values. Therefore, MRHM was superior to other three models in describing the photosynthetic response curve, the accurate values were that the quantum efficiency (α), maximum net photosynthetic rate (Pmax), light saturation point (LSP), light compensation point (LCP) and respiration rate (Rd) were 0.06, 6.06 μmol·m-2s-1, 802.68 μmol·m-2s-1, 10.76 μmol·m-2s-1 and 0.60 μmol·m-2s-1. Moreover, the photosynthetic response parameters values among different layers were also significant. Our findings have critical implications for parameter calibration of photosynthetic models and thus robust prediction of photosynthetic response in forests.

Phase Role in the Non-Uniformity of Main-Line Couplings in Asymmetric Extracted-Pole Inline Filters

The use of classical symmetrical polynomial definition to synthesize fully canonical inline filters with an asymmetrical distribution of the transmission zeros along the topology leads to the occurrence of uneven admittance inverter in the main-line. This form introduces some limitations to transform such topology into a ladder network. Despite circuital transformation can be used to accommodate both technology and topology, it is usual that extra reactive elements are necessary to implement phase shifts required to achieve the complete synthesis. This article introduces a novel method able to determine the required phase correction that has to be applied to the characteristic polynomials in order to equalize all the admittance inverters in the main path to the same value. It has been demonstrated that a suitable pair of phase values can be accurately estimated using a developed hyperbolic model which can be obtained from the transmission and reflection scattering parameters. To experimentally validate the proposed method, a Ladder-type filter with asymmetrical polynomial definition has been synthesized, fabricated, and measured, demonstrating the effectiveness of the developed solution.

Localized stationary seismic waves predicted using a nonlinear gradient elasticity model

This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behavior is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend) as well as localized stationary waves are found by analyzing the obtained ordinary differential equation in the phase portrait and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.

Creep Behavior of Saturated Clay in Triaxial Test and a Hyperbolic Model

As one of the basic mechanical properties of soil, the creep property of a given type soil is related to stress path, and stress level. In this paper, triaxial shear creep tests under different deviatoric stress levels were performed on both intact sample and the reconstituted sample of clay taken from Hangzhou, China. Based on the Boltzmann linear superposition principle, the creep curves of the clay sample under different levels of deviatoric stress were obtained, and the creep characteristics of the intact sample and the reconstituted sample were compared in both total stress creep analysis and effective stress creep analysis. Furthermore, the creep curves were fitted using a hyperbolic creep model. The results show that (1) under the same stress level, the creep of intact sample evolves more than that of reconstituted sample; (2) the hyperbolic creep model is suited to describe the creep characteristics of intact and reconstituted clay, and the model parameters A s and B s can be linearly correlated to the stress level D r ; (3) for the application of the hyperbolic model, the total stress analysis works better, and the model parameters A s and B s can be determined by a linear relationship with Dr.

Investigation of the Mechanical Behavior of Polypropylene Fiber-Reinforced Red Clay

Red clay is not easy to use as a natural foundation because of its high water content, high plasticity index, large void ratio, and susceptibility to shrinkage and cracking. In this study, consolidated undrained triaxial tests were conducted to examine the mechanical properties of polypropylene fiber-reinforced red clay and to analyze the influence of the fiber content (FC), fiber length (FL), and cell pressure on its shear strength. By performing a regression analysis on the test data, a hyperbolic constitutive model that considers the influence of FC, FL, and cell pressure was established, and a method was developed to estimate the parameters of the model. The findings show that, in contrast with the nonreinforced red clay, the fiber-reinforced red clay had a stress-strain curve characterized by typical strain hardening, with the shear strength increasing with FC, FL and cell pressure. The calculated results of the model coincide with the test results well, confirming that the hyperbolic model could appropriately describe the stress-strain relationship of polypropylene fiber-reinforced red clay and have reference value for the design and construction of fiber-reinforced red clay foundations.

Quantitative Assessment of the Development of Micromycete Colony on the Surfaces of Polymers and Polymer Composites

The need to ensure the possibility of widespread use of electronic and mobile health-saving technologies requires not only the formation of an appropriate information technology infrastructure and the development of effective algorithms for processing a large amount of personal information. Development of medical devices for recording physiological processes also involves the creation of innovative biologically compatible materials that allow sensors and medical sensors to work continuously in 24/7 mode. Taking into account the long-term positive experience of using large-capacity thermoplastics and elastomers in medical equipment, it seems promising to use the corresponding polymers as the main materials of wearable electronics for medical purposes. At the same time, to ensure the biological compatibility of the materials under discussion, it is necessary to minimize the possibility of the development of pathogenic microorganisms on surfaces in contact with living tissues. This type of pathogenic organisms (pathogens of a number of dangerous diseases – mycoses) includes some types of microscopic fungi - micromycetes (in particular, Aspergillus niger van Tiegem; Aspergillus terreus Thom; Penicillium cycopium Westling). The article examines the effect of surface modification by gas-phase fluorination on the nature and degree of development of a mixed colony of micromycetes on the surfaces of experimental samples made of several types of thermoplastics (polyvinyl chloride, polypropylene, low-density polyethylene, polyethylene terephthalate) and elastomers (butyl- and butadiene-nitrile rubbers, as well as ethylene, propylene and dicyclopentadiene copolymers). The nature and degree of development of colonies are quantitatively described using the original methodology developed earlier. The effect of fluorination on the nanotexture and chemical composition of the surface and near-surface layers of experimental samples was demonstrated using scanning electron microscopy (SEM) and IR Fourier spectroscopy (IRFS). The dynamics and efficiency of fluorination are described using a linearized hyperbolic model, the parameters of which are set by the least squares method.

On the global existence and time-decay rates for a parabolic–hyperbolic model arising from chemotaxis

In this paper, we are concerned with the study of the Cauchy problem for a parabolic–hyperbolic model arising from chemotaxis in any dimension [Formula: see text]. We first prove the global existence of the model in [Formula: see text] critical regularity framework with respect to the scaling of the associated equations. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we also establish the time-decay rates for the constructed global solutions. Our analyses mainly rely on Fourier frequency localization technology and on a refined time-weighted energy inequalities in different frequency regimes.

Experimental Study on the Shearing Behaviour on the Interface between Coarse Sand and Concrete under High Stress

The shear behaviour on the interface between soil and structure is a research hot point. Based on the RMT-150B rock mechanics test system, a series of high-stress direct tests were performed on the coarse sand under the condition of different moisture contents and concrete substrates with different rough and hardness. The results showed that the shear stress-displacement curve and volumetric strain-displacement curve of the interface under high stress could be fitted by a hyperbolic model; the ultimate shear strength and initial shear stiffness of the interface both increased with the normal stress while the shear stiffness decreased with the shear displacement. The crushing rate of the coarse sand particles on the interface increased with the normal stress. After the range analysis for the influencing factors of the interface’s shearing behaviour, it was shown that for the ultimate shear strength, their sequence of influencing degree was normal stress, the roughness of interface, moisture content, and hardness of concrete base; for the initial shear strength, the sequence was normal stress, moisture content, interface roughness, and basal hardness. As for dry sand, the possibility of relative particle crushing was higher than that of sand with a moisture content of 8%, and a peak of crushing occurred when the moisture content was 16%.