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.

GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.

Differentially Private Real-Time Streaming Data Publication Based on Sliding Window Under Exponential Decay

Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure.The existing research on differential privacy streaming data publication mostly pay close attention to boosting query accuracy,but pay less attention to query efficiency,and ignore the effect of timeliness on data weight.In this paper,we propose an effective algorithm of differential privacy streaming data publication under exponential decay mode.Firstly,by introducing the Fenwick tree to divide and reorganize data items in the stream,we achieve a constant time complexity for inserting a new item and getting the prefix sum.Meanwhile,we achieve time complicity linear to the number of data item for building a tree.After that,we use the advantage of matrix mechanism to deal with relevant queries and reduce the global sensitivity.In addition,we choose proper diagonal matrix further improve the range query accuracy.Finally,considering about exponential decay,every data item is weighted by the decay factor.By putting the Fenwick tree and matrix optimization together,we present complete algorithm for differentiate private real-time streaming data publication.The experiment is designed to compare the algorithm in this paper with similar algorithms for streaming data release in exponential decay.Experimental results show that the algorithm in this paper effectively improve the query efficiency while ensuring the quality of the query.

EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.

Exponential decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast

To investigate decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast,a new exponential decay(ED)law was proposed.The results show that the micro-fracture activity decay law after multistage stress loading and blasting disturbance conforms to the ED model,in which the sum of A and n represents the number of initial micro-fracture events,and n represents the level of background micro-fracture events.The ED model can describe the number of initial micro-fracture events with a deviation less than 10%.The ED model outperforms the traditional aftershock models in describing the micro-fracture event decay law in the three cases considered.The ED model can provide a reference for selecting the blasting interval in mines,which is of great significance to maintain the stability of the surrounding rock and ensure safe production in metal mines.

GLOBAL STRONG SOLUTION AND EXPONENTIAL DECAY OF 3D NONHOMOGENEOUS ASYMMETRIC FLUID EQUATIONS WITH VACUUM

We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.

On the Exponential Decay of Solutions for Some Kirchhoff-Type Modelling Equations with Strong Dissipation

This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global existence of solutions by constructing a stable set in and show the energy exponential decay estimate by applying a lemma of V. Komornik.

Potential Response Analysis of Exponentially Decaying Polarizing Current of Electrode and its Use in the Study of Stress Corrosion Cracking(SCC)of Stainless Steel

A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensured from theoretical analysis,and this is the theoretical foundation of the critical point method for the measurement of corrosion current of metals.The comparison of the corrosion currents measured by the critical point and static methods for the system of 321 stainless steel in 0.5N HCI+0.5N NaCI solution at static state shows that the results agree very well.Finally.the tran- sient corrosion currents of 321 stainless steel in 0.5N HCI+0.5N NaCl solution at different strain level are listed.

Applications of exponential decay and geometric series in effective medicine dosage

The problem facing by physicians is the fact that for most drugs there is a minimum concentration below which the drug is ineffective, and a maximum concentration above which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its concentration in bloodstream of a patient. For analysis of dose concentration and mathematical mo- delling of minimum and maximum concentration of a drug administered intravenously, the EDM (Exponential Decay Model) and GSF (Geometric Series and its Formula) are the powerful mathematical tools. In the present research study, these two mathematical tools were used to predict the dose concentration of a drug in bloodstream of a patient.

Predefined Exponential Basis Set for Half-Bounded Multi Domain Spectral Method

A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.

ASYMPTOTIC BEHAVIOUR AND EXPONENTIAL STABILITY FOR THERMOELASTIC PROBLEM WITH LOCALIZED DAMPING

A semi-linear thermoelastic problem with localized damping is considered, which is one of the most important mathematical models in material science. The existence and decays exponentially to zero of solution of this problem are obtained. Moreover, the existence of absorbing sets is achieved in the non-homogeneous case. The result indicates that the system which we studied here is asymptotic stability.

Uniform Exponential Stabilization for Flexural Vibrations of a Solar Panel

Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.

A Phenomenological Model for Decay Process of Long-Persistent Phosphorescence

A sum of two or more exponential decay functions is empirically adopted nowadays to analyze the decay curve of long-persistent phosphor.However,the fitting parameters of this empirical model lack well-defined physical meanings,especially when the number of exponential decay function is greater than two.We propose a phenomenological model to describe the decay curve oflong-persistent phosphor based on an analysis of the relationship between carrier concentration and light-emitting intensity.This model has a few fitting parameters with well-defined physical meanings as compared to the current empirical one.With this model,we quantitatively analyze the decay processes of typical long-persistent phosphors of SrAl_(2)O_(4):Eu,Dy and obtain reasonable fitting results.

EXPONENTIAL FOURIER COLLOCATION METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATIONS

In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.

General decay of energy to a nonlinear viscoelastic two-dimensional beam

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.

Differential Calculus the Study of the Growth and Decay of an Entity’s Population

Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, i.e. when the resources are unlimited, a population P believes according to the following differential equation P’ = KP, with the application of the differential calculus we obtasin an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

Efficiency of a Modular Cleanroom for Space Applications

A prototype cleanroom for hazardous testing and handling of satellites prior to launcher encapsulation,satisfying the ISO8 standard has been designed and analyzed in terms of performances.Unsteady Reynolds Averaged Navier-Stokes(URANS)models have been used to study the related flow field and particulate matter(PM)dispersion.The outcomes of the URANS models have been validated through comparison with equivalent large-eddy simulations.Special attention has been paid to the location and shape of the air intakes and their orientation in space,in order to balance the PM convection and diffusion inside the cleanroom.Forming a cyclone-type flow pattern inside the cleanroom is a key to maintaining a high ventilation efficiency.

LOW-REGULARITY SOLUTIONS TO FOKKER-PLANCK-TYPE SYSTEMS IN THE WHOLE SPACE

In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).

Global Existence and Exponential Decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping

In this paper we investigate a nonlinear viscoelastic equation with nonlinear damping. Global existence of weak solutions and uniform decay of the energy have been established. The Faedo-Galerkin method and the perturbed energy method are employed to obtain the results.

Partial discharge characteristics of an air gap defect in the epoxy resin of a saturable reactor under an exponential decay pulse voltage

Saturable reactor insulation is currently stressed by an exponential decay pulse voltage under normal operating conditions.The partial discharge(PD)characteristics of epoxy resin under an exponential decay pulse voltage were studied here and were compared at 25 and 110℃.In addition,this study compares these PD characteristics with those under a sinusoidal voltage to better measure the insulation design margin of the saturable reactor under an exponential decay pulse voltage.Finally,this study explains the PD mechanism based on the three-capacitor circuit model and space charge accumulation.Compared with the sinusoidal voltage,a higher amplitude,a higher inception voltage and fewer PDs are obtained under the pulse voltage.The reason may be related to the accumulation of space charge.Due to the duality of the space charge effect,the promotion effect of space charge accumulation on the PD under the pulse voltage is dominant,and an increase in temperature will weaken the promotion effect.In contrast,the inhibitory effect of space charge accumulation on the PD under the sinusoidal voltage is dominant.The experimental results can provide a basis for the optimal design of saturable reactor insulation under an exponential decay pulse voltage.