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The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis R e f f (m) = 9 and effective reproduction numbers of pneumonia R e f f (p) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is m a x R e f f m , R e f f (p) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are α 1 , α 2 and π . Biologically, decrease in α 1 and increasing in π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities. [ABSTRACT FROM AUTHOR]

A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis. [ABSTRACT FROM AUTHOR]