General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback

In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases.Comment: 11 page

On a Kelvin-Voigt Viscoelastic Wave Equation with Strong Delay

An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin & Voigt-type material law is considered. Transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued $C^{0}$- and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using the Lyapunov's indirect method. The singular limit $\tau \to 0$ is further studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.Comment: 34 pages, 4 figures, 1 set of Matlab code

Economic Analysis and Willingness to Pay for Alternative Charcoal and Clean Cook Stoves in Haiti

Conventional charcoal and firewood are the main source of energy in Haiti. They provide up to 90% of the country’s energy for domestic and industrial use, resulting in severe environmental and health issues. The present study is initiated to better understand the reasons why two promising alternative technologies (improved cookstoves and alternative charcoal briquettes) have experienced low adoption in Haiti. The research was carried out in two districts in southern Haiti where the improved stoves and briquettes production units exist and where households benefited from a program distributing the improved stoves. This project contributes to the literature by gauging interest in the improved stove and briquettes, as well as their specific characteristics. It helps understand factors that affect the adoption and dis-adoption of the technologies. Additionally, the research measures tangible benefits for households that adopted the improved stoves. The study reveals that the use of the improved stoves lowers fuel expenditures by 14.6 cents/day to 23.6 cents/day. Haitian consumers are interested in both the stove and briquettes, but their willingness-to-pay depends on their personal characteristics such as location and income. The study has revealed two surprising results as well: Unnecessary dis-adoption of the stoves occurs because the two technologies were needlessly marketed together. Despite the target audience, which is poor and rural consumers, the improved stove is perceived as a rich, urban user’s technology

EFFECTS OF AGRICULTURAL LOANS IN DEVELOPING COUNTRIES – BENIN CASE STUDY

Limited access to financial services is known as a major constraint to agricultural development (FAO, 2002). Farmers need liquidity to face agricultural expenses throughout the production cycle but mainly at the beginning. Mainstream financial institutions are reluctant to serve the agricultural sector for several reasons. First, they consider the sector to be highly risky with low performance. Also, agricultural activities depend on the weather, they take place in remote rural areas, and commodities prices are volatile. All these aspects make it hard for standard banks to reach their profit goals when lending to farmers. Since microfinance was conceived, it has generated a lot of hope for alleviating poverty in low-income countries. Microfinance provides the poor with access to affordable capital by granting low-income individuals with loans they would not otherwise have access to, because of economic and geographic constraints. The goal of the dissertation is to examine the role and the importance of microfinance in the agricultural sector of developing countries. A survey took place in October 2017, in both rural and urban areas of Benin and involved 750 agricultural households. Three different agricultural zones were selected: the North-East (cotton zone); the Center (tubers and cashew nut zone) and the South (a region with special crops such as vegetables, pineapple, palm tree, exotic plants). The study focuses on agricultural loans. It includes clients of the major microfinance institution in Benin: FECECAM - Faîtière des Caisses d’Epargne et de Crédit Agricole Mutuel. This research contributes to the literature in several ways. The study allows shedding light on the effects of agricultural loans, specifically, on households’ efficiency and labor employment, which are mostly overlooked in the microfinance literature. To overcome selection bias in microcredit evaluation, the research employs a pipeline design. Control and treatment groups consist of individuals who have chosen to participate in the microfinance program. The loan treatment considered is the experience with loans which includes program entry timing, loan take-up frequency, and the average amount of loan obtained over the 2012-2017 period. The study employs a cluster analysis technique to create reliable comparable groups. Multiple variables and indicators are analyzed. A descriptive analysis of loan impact on farmers’ labor input choices shows that past loans have residual effects on both hired and family labor use. Farm loans, especially those obtained for farm machinery significantly reduce expenditure on hired labor but more family labor is employed using machine loans while other loan categories reduced the use of family labor. The evaluation of the whole-farm efficiency of borrowers in the presence of agricultural loans reveals significant technical and allocative errors leading to profit loss in all studied regions. However, experience with loans significantly increases farmers’ whole-farm efficiency, particularly in the North. Finally, the assessment of well-being indicators suggests that those farm loans have a significant positive impact on sampled recipients’ net farm income, food security and food quality statuses. Agricultural loans also have a positive impact on women’s empowerment. The monitoring and implementation mechanism of FECECAM played a crucial role in the success of its loan programs

Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors

Some multilevel methods on graded meshes

AbstractWe consider Yserentant's hierarchical basis method and multilevel diagonal scaling method on a class of refined meshes used in the numerical approximation of boundary value problems on polygonal domains in the presence of singularities. We show, as in the uniform case, that the stiffness matrix of the first method has a condition number bounded by (ln(1/h))2, where h is the meshsize of the triangulation. For the second method, we show that the condition number of the iteration operator is bounded by ln(1/h), which is worse than in the uniform case but better than the hierarchical basis method. As usual, we deduce that the condition number of the BPX iteration operator is bounded by ln(1/h). Finally, graded meshes fulfilling the general conditions are presented and numerical tests are given which confirm the theoretical bounds

Dirichlet problems in polyhedral domains II: Approximation by FEM and BEM

AbstractThe convergence of the classical finite element method (FEM) and boundary element method (BEM) is poor due to the edge and vertex singularities of the solution of the involved Dirichlet problem relative to an elliptic operator in a polyhedron. Using the global regularity results of Lubuma and Nicaise (1994), we analyse refined FEM and BEM with optimal rates of convergence