The aim of this paper was to obtain a new model for the bending-stretching of an anisotropic heterogeneous linearly piezoelectric cantilever rod when the electric potential is applied on the both ends. The process is assumed to be static, and the piezoelectric material is monoclinic of class 2. To derive the model, we start with the corresponding threedimensional problem, introduce a change of variable together with a scaling of the unknowns and then we use a passage to the limit procedure, based on arguments of asymptotic analysis taking the diameter of the cross-section as small parameter. Finally, we prove a result of strong convergence that justifies both the method and the one-dimensional model obtained. One of the most relevant features of this one-dimensional model is that the stretching is coupled with the electric potential, while the bendings are not.Mathematics Subject Classification (2010). Primary 74K10; Secondary 41A60 · 35C20 · 35Q60.

We construct a mathematical model of kinetic type in order to describe the immune system interactions in the context of autoimmune disease. The interacting populations are self-antigen presenting cells, self reactive T cells and the set of immunosuppressive cells consisting of regulatory T cells and Natural Killer cells. The main aim of our work is to develop a qualitative analysis of the model equations and investigate the existence of biologically realistic solutions. Having this goal in mind we describe the interactions between cells during an autoimmune reaction based on biological considerations that are given in the literature and we show that the corresponding system of integro-differential equations has finite positive solutions. The asymptotic behaviour of the solution of the system is also studied. We complement our mathematical analysis with numerical simulations that study the sensitivity of the model to parameters related to proliferation of immunosuppressive cells, destruction of self-antigen presenting cells and self reactive T cells and tolerance of SRTCs to self-antigens.

Articles you may be interested inA general methodology for inverse estimation of the elastic and anelastic properties of anisotropic open-cell porous materials-with application to a melamine foam J. Appl. Phys. 115, 084904 (2014); 10.1063/1.4865789 Rheology of viscoelastic suspensions of spheres under small and large amplitude oscillatory shear by numerical simulationsAbstract. In this paper, we show how fractional viscoelastic models can be efficient in the modeling of linear viscoelastic behavior, increasing the fitting accuracy of classic generalized viscoelastic models, such as the Generalized Maxwell model. Experimental data (Loss and Storage modulus in the frequency domain) were retrieved from a Dynamic Mechanical Analysis test considering Carbon Fibre Reinforced Polymer samples. The estimated parameters, for the derived fractional viscoelastic models, were obtained through numerical optimization techniques that minimize the difference between model-predicted values and experimental data. An excellent correlation between analytical and experimental results was observed, minimizing numerical instabilities found on a previous work, for the same experimental setup.

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CoronaVac(SARS-CoV-2 inactivated vaccine) has been largely used as the main immunogen for COVID-19 in several countries. However, its immunogenicity in immunocompromised individuals has not been established. This was a prospective controlled study of 910 adult ARD patients and 182 age- and sex-matched control group(CG) who received two doses of CoronaVac in a 28-days interrval. Anti-SARS-Cov-2 IgG and neutralizing antibodies were assessed at each vaccine shot and 6 weeks after the 2nd dose. Vaccine adverse events(AE) were similar in both groups. We observed significant lower anti-SARS-Cov-2 IgG seroconversion(70.4% vs. 95.5%,p < 0.001) and titers[12.1(95%CI 11.0-13.2) vs. 29.7(95%CI 26.3–33.5),p < 0.001], frequency of neutralizing antibodies(56.3% vs. 79.3%),p < 0.001) and median (interquartile range) neutralization activity [58.7(43.1–77.2) vs. 64.5(48.4–81.4),p = 0.013] in ARD patients compared to CG. A significant decline in the number of COVID-19 cases (p < 0.0001) were observed 10 days after the second dose, with a predominant P1 variant. Safety analysis revealed no moderate/severe AEs. In conclusion, CoronaVac has an excellent safety profile and reasonable rates of quantitative serology(70.4%)/neutralization(56.3%) in ARD patients. The impact of this reduced immunogenicity in vaccine effectiveness warrants further evaluation.

In this work, and based on numerical optimization techniques, constitutive parameters for viscoelastic materials are determined using a inverse problem formulation. The optimization methodology is based on experimental results obtained in the frequency domain, for a CFRP-Carbon Fibre Reinforced Polymer, through DMA-Dynamic Mechanical Analysis. The relaxation modulus of viscoelastic materials is given by a summation of decaying exponentiating functions, known as Prony series. Prony series, in time domain, are normally used to determine constitutive parameters for viscoelastic materials. In this paper, using the Fourier transform of the time domain Prony series, a nonlinear constrained least square problem based on Prony series representations of storage and loss modulus, for the considered material, is analyzed. A case study considering the estimation of 2N viscoelastic parameters, N = 1, 2, • • •11, is taken as a benchmark. The nonlinear constrained least square problems are solved using global and local optimization solvers. The computational results as well as the main conclusion are shown.

In this paper we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in the model in a proper way. For both time dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen-Chlorine system as reference. Several numerical computations are included illustrating the behaviour of the phase velocity and attenuation coefficient in a low frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.

Abstract. In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. This planning was modelled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfils the cultivation water requirements. In this paper, we characterize the solution of our problem guaranteeing the existence of the solution and applying the necessary and sufficient conditions of optimality. We validate the numerical results obtained previously, comparing the analytical and numerical solutions.