The Effect of the First order Responses of Mooring Line on the Second order Mooring Line Damping

In this paper we investigated the effect of the first order responses of mooring line on the second order mooring line damping.In the study of the slow oscillating of a moored floating structure by perturbation method in frequency domain,the second order equations of the mooring line are divided into non homogeneous and homogeneous equations.The solutions are related to the first order responses of mooring line and second order floating structure oscillation respectively.In order to find the effect of the first order responses of mooring line,the second order mooring line tension and damping were determined by solving the non homogeneous equation and homogeneous equation.From the results,we found,although the second order mooring line tension obtained from the non homogenous equation is quite small compared with the total second order mooring line tension,the damping contributed from both of them are in the same order in quantity.So,in predicting the second order mooring line damping,the effect of the solution related to the non homogeneous equation can not be omitted.

Estimation of Landfill Gas and Its Renewable Energy Potential from the Polesgo Controlled Landfill Using First-Order Decay (FOD) Models

Methane generation in landfills and its inadequate management represent the major avoidable source of anthropogenic methane today. This paper models methane production and the potential resources expected (electrical energy production and potential carbon credits from avoided CH4 emissions) from its proper management in a municipal solid waste landfill located in Ouagadougou, Burkina Faso. The modeling was carried out using two first-order decay (FOD) models (LandGEM V3.02 and SWANA) using parameters evaluated on the basis of the characteristics of the waste admitted to the landfill and weather data for the site. At the same time, production data have been collected since 2016 in order to compare them with the model results. The results obtained from these models were compared to experimental one. For the simulation of methane production, the SWANA model showed better consistency with experimental data, with a coefficient of determination (R²) of 0.59 compared with the LandGEM model, which obtained a coefficient of 0.006. Thus, despite the low correlation values linked to the poor consistency of experimental data, the SWANA model models methane production much better than the LandGEM model. Thus, despite the low correlation values linked to the poor consistency of the experimental data, the SWANA model models methane production much better than the LandGEM V3.02 model. It was noted that the poor consistency of the experimental data justifies these low coefficients, and that they can be improved in the future thanks to ongoing in situ measurements. According to the SWANA model prediction, in 27 years of operation a biogas plant with 33% electrical efficiency using biogas from the Polesgo landfill would avoid 1,340 GgCO2e. Also, the evaluation of revenues due to electricity and carbon credit gave a total revenue derived from methane production of US$27.38 million at a cost of US$10.5/tonne CO2e.

Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

A Simple Method of Solving First-order Indefinite Equa tion

The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.

Conformal invariance and Hojman conserved quantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Research on Precise Trigonometric Leveling in Place of First Order Leveling

Through the analysis of the principle, error sources and precision of trigonometric leveling, this paper points out the key problems about first order leveling replaced by trigonometric leveling; and for the first time puts forward that, in some given conditions, it is not only feasible but also valuable to replace first order leveling by precise trigonometric leveling, and proves it by experimentation as well. The content and conclusion of this paper have consulting significance and practicable value for our setting down relational criterion and production practice.

Active disturbance rejection control on first-order plant

Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection control（LADRC） scheme is presented to cope with the difficulties,and a reduced-order observer scheme is proposed further.Some quantitative dynamic results with regard to non-overshoot characteristics are obtained.Finally,the performance boundaries of LADRC and PI control are explicitly compared with each other,which shows that the former is more superior in most cases.

Consensus problems of first-order dynamic multi-agent systems with multiple time delays

Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.

Application of first order rate kinetics to explain changes in bloom toxicity——the importance of understanding cell toxin quotas

Cyanobacteria are oxygenic photosynthetic Gram-negative bacteria that can form potentially toxic blooms in eutrophic and slow flowing aquatic ecosystems. Bloom toxicity varies spatially and temporally, but understanding the mechanisms that drive these changes remains largely a mystery. Changes in bloom toxicity may result from changes in intracellular toxin pool sizes of cyanotoxins with differing molecular toxicities, and/or from changes in the cell concentrations of toxic and non-toxic cyanobacterial species or strains within bloom populations. We show here how first-order rate kinetics at the cellular level can be used to explain how environmental conditions drive changes in bloom toxicity at the ecological level. First order rate constants can be calculated for changes in cell concentration( μ_c : specific cell division rate) or the volumetric biomass concentration( μ_g : specific growth rate) between short time intervals throughout the cell cycle. Similar first order rate constants can be calculated for changes in nett volumetric cyanotoxin concentration( μ_(tox) : specific cyanotoxin production rate) over similar time intervals. How μ_c(or μ_g) covaries with μ tox over the cell cycle shows conclusively when cyanotoxins are being produced and metabolised, and how the toxicity of cells change in response to environment stressors. When μ_(tox)/μ_c >1, cyanotoxin cell quotas increase and individual cells become more toxic because the nett cyanotoxin production rate is higher than the cell division rate. When μ_(tox)/μ_c =1, cell cyanotoxin quotas remains fixed because the nett cyanotoxin production rate matches the cell division rate. When μ_(tox)/μ_c <1, the cyanotoxin cell quota decreases because either the nett cyanotoxin production rate is lower than the cell division rate, or metabolic breakdown and/or secretion of cyanotoxins is occurring. These fundamental equations describe cyanotoxin metabolism dynamics at the cellular level and provide the necessary physiological background to understand how environmental stressors drive changes in bloom toxicity.

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

First-order Derivative Spectrophotometry for the Determination of Vitamin C in Medicament

A novel method for the determination of vitamin C（Vc） is proposed in this article. After the reaction with Folin-Ciocalteau reagent at ambient temperature, Vc solution was scanned at 750--1100 nm, and its first-order derivative spectrum were obtained from the original spectrum. The values of derivative selected at 995 nm were used for determination. It was proved that Vc could quickly react with Folin-Ciocalteau reagent within 5 min and the product was quite stable for a long time. The conditions required for this method is not very complicated, its precision and accuracy are similar to those of the iodometric titration described in Chinese Pharmacopoeia, and the limit of detection is 0.312 μg/mL. The determination of the results of vitamin C tablet, pill, and injection demonstrates that this method has wide pharmaceutical applications.

Characteristic-knowledge-aided spectral detection of high frequency first-order sea echo

To detect high frequency （HF） first-order sea echo spectra contaminated with ships, ionosphere interference, and other, a new characteristic-knowledge-aided detection method is proposed. With 2-D image features in range-Doppler spectrum, the trend of first-order sea echoes is extracted as indicative information by a multi-scale filter. Detection rules for both single and splitting first-order sea echoes are given based on the characteristic knowledge combining the indicative information with the global characteristics such as amplitude, symmetry, continuity, etc. Compared with the classical algorithms, the proposed method can detect and locate the first-order sea echo in the HF band more accurately especially in the environment with targets/clutters smearing. Experiments with real data verify the validity of the algorithm.

Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations

Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.

First Order Phase Transitions as Radiation Processes

This paper presents new experimental evidence of the PeTa effect—infrared characteristic radiation under first order phase transitions, especially the crystallization of melts and the deposition and condensation of vapours/gases. The PeTa effect describes the transient radiation that a particle (i.e., atom, molecule or/and cluster) emits transient radiation during a transition from a meta-stable higher energetic level (in a super-cooled melt or a super-saturated vapour) to the stable condensed lower level (in a crystal or a liquid). The radiation removes latent heat with photons of characteristic frequencies that are generated under this transition. The abbreviation “PeTa effect” means Perel’man-Tatartchenko’s effect.

First Order Phase Transitions as Radiation Processes, Part Two

This paper presents new experimental results concerning the PeTa effect—infrared characteristic radiation under first order phase transitions, especially during deposition and condensation of vapours/gases and the crystallisation of melts. The abbreviation “PeTa effect” means Perel’man-Tatartchenko’s effect. The nature of the PeTa effect is transient radiation that a particle (i.e., atom, molecule or/and cluster) emits during a transition from a meta-stable higher energetic level (in a super-cooled melt or super-saturated vapour) to the stable condensed lower level (in a crystal or liquid). The radiation removes latent heat with photons of characteristic frequencies that are generated under this transition. This paper is the second in a set describing the appearance of PeTa radiation under air cooling with deposition and condensation of air components. The radiation was recorded using an IR Fourier Spectrometer with a highly sensitive MCT detector. Certain peculiarities of the recorded radiation as well as its applications in the physics of the atmospheres of Earth and Jupiter are analysed.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

Discrete Methods Based on First Order Reversal Curves to Identify Preisach Model of Smart Materials

Preisach model is widely used in modeling of smart materials. Although first order reversal curves （FORCs） have often found applications in the fields of physics and geology, they are able to serve to identify Preisach model. In order to clarify the relationship between the Preisach model and the first order reversal curves, this paper is directed towards： （1） giving the reason a first order reversal curve is introduced; （2） presenting, for identifying Preisach model, two discrete methods, which are analytically based on first order reversal curves. Herein also is indicated the solution＇s uniqueness of these two identifying methods. At last, the validity of these two methods is verified by simulating a real smart actuator both methods have been applied to.

THE INITIAL VALUE PROBLEMS OF FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, by using of monotone iterative technique, the existence and iterative approximation of the minimax quasi_solutions of the initial value problems for more general first order impulsive differential equations in Banach spaces are investigated.

A first order system model of fracture healing

A first order system model is proposed for simulating the influence of stress stimulation on fracture strength during fracture healing. To validate the model, the diaphyses of bilateral tibiae in 70 New Zealand rabbits were osteotomized and fixed with rigid plates and stress-relaxation plates, respectively. Stress shielding rate and ultimate bending strength of the healing bone were measured at 2 to 48 weeks postoperatively. Ratios of stress stimulation and fracture strength of the healing bone to those of intact bone were taken as the system input and output. The assumed first order system model can approximate the experimental data on fracture strength from the input of stress stimulation over time, both for the rigid plate group and the stress-relaxation plate group, with different system parameters of time constant and gain. The fitting curve indicates that the effect of mechanical stimulus occurs mainly in late stages of healing. First order system can model the stress adaptation process of fracture healing. This approach presents a simple bio-mathematical model of the relationship between stress stimulation and fracture strength, and has the potential to optimize planning of functional exercises and conduct parametric studies.