An experimental study of wall-injected flows in a rectangular cylinder

An experimental investigation of the flow inside a rectangular cylinder with air injected continuously along the wall is performed. This kind of flow is a two-dimensional approximation of what happens inside a solid rocket motor, where the lateral grain burns expelling exhaust gas or in processes with air filtration or devices to attain uniform flows. We propose a brief derivation of some analytical solutions and a comparison between these solutions and experimental data, which are obtained using the Particle Image Velocimetry (PIV) technique, in order to provide a global reconstruction of the flowfield. The flow, which enters orthogonal to the injecting wall, turns suddenly its direction being pushed towards the exit of the chamber. Under the incompressible and inviscid flow hypothesis, two analytical solutions are reported and compared. The first one, known as Hart-McClure solution, is irrotational and the injection velocity is non-perpendicular to the injecting wall. The other one, due to Taylor and Culick, has non-zero vorticity and constant, vertical injection velocity. The comparison with laminar solutions is useful to assess whether transition to turbulence is reached and how the disturbance thrown in by the porous injection influences and modifies those solutions

Linear Sobolev Type Equations with Relatively -Sectorial Operators in Space of "Noises"

The concept of "white noise," initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of "noises" are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable "noises." The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Smartphone and social network addiction in early adolescents: The role of self-regulatory self-efficacy in a pilot school-based intervention

Background: Youths' online problematic behaviors, such as smartphone or social network sites (SNS) addiction, gained increasing attention nowadays, due to their impact on concurrent and later adjustment, such as emotional and/or behavioral problems, academic impairments, or relational issues. Aims: This study aims to evaluate the effectiveness of a pilot school-based intervention to contrast online addictive behaviors while fostering adolescents' self-regulative abilities. Materials & Methods: The intervention started in January 2022 in an Italian junior high school located in Rome, and consisted of four meetings with students. A total sample of 462 15-year-old adolescents (Mage = 15.2; SD = 0.50; 41% females; Ncontrol = 214; Nintervention = 248) was considered. Within the latent difference score framework, we examined short-term changes from the pre-to-the-postintervention levels of SNS and smartphone addiction, and self-regulatory self-efficacy (SRSE) beliefs as a possible booster of the intervention's effectiveness. Results: Results showed a significant decrease in both online addictions (SNS and smartphone addiction), controlling for age, gender, sexual orientation, and socioeconomic status, because of the short-term efficacy of the project. The buffering effect of SRSE beliefs was further supported. Conclusion: These findings emphasized the usefulness of promoting youths' self-regulative beliefs to contrast problematic tendencies, according to a Positive Youth Development perspective which focused on resources rather than only on the prevention of negative outcomes for youths' adjustment

Exploring the protective function of positivity and regulatory emotional self-efficacy in time of pandemic covid-19

Despite several empirical studies on the 2019 coronavirus disease (COVID-19) pandemic that have highlighted its detrimental effect on individuals’ mental health, the identification of psychological factors that may moderate its impact on individuals’ behavior and well-being remains partly unexplored. The present study was conceived to examine the mediation role of regulatory emotional self-efficacy in the relationship between positivity and anxiety, depression, and perceived self-efficacy in complying with the containment measures to contrast the COVID-19 spread. Furthermore, the moderation role of age was tested. A sample of 1258 participants (64.2% women; Mage = 42.09, SD = 13.62) enrolled from the Italian general population answered an online survey aimed at investigating the role of individual differences in facing the COVID-19 pandemic. We opted for a snowball recruiting procedure to find participants. The online survey was disseminated through email invitation and using social media platforms (i.e., Facebook, Instagram). A multi-group path analysis model was performed using Mplus 8.4 to explore the hypothesized relations among variables. The following criteria were employed to evaluate the goodness of fit: χ2 likelihood ratio statistic, CFI and TLI > 0.95, RMSEA < 0.06 and SRMR < 0.08. The findings corroborated the protective role of both positivity and regulatory emotional self-efficacy in reducing individuals’ anxiety and depressive symptoms, as well as in fostering individuals’ capabilities in complying with the containment measures imposed by the government to reduce the risk of illness and to contain the spread of the virus COVID-19. Specifically, regulatory emotional self-efficacy beliefs partially mediated the relations between positivity and anxiety and depressive symptoms and fully mediated the effect of positivity on perceived self-efficacy beliefs in complying with the containment measures. These paths were equal across ages. The results of the present study appear relevant to implementing psychological interventions aimed to reduce the deleterious effects of the COVID-19 pandemic on mental health through the promotion of individuals’ optimistic orientation and emotion regulation

Well-posedness for degenerate third order equations with delay and applications to inverse problems

[EN] In this paper, we study well-posedness for the following third-order in time equation with delay <disp-formula idoperators defined on a Banach space X with domains D(A) and D(B) such that t)is the state function taking values in X and u(t): (-, 0] X defined as u(t)() = u(t+) for < 0 belongs to an appropriate phase space where F and G are bounded linear operators. Using operator-valued Fourier multiplier techniques we provide optimal conditions for well-posedness of equation (0.1) in periodic Lebesgue-Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel-Lizorkin spaces Fp,qs(T,X). A novel application to an inverse problem is given.The first, second and third authors have been supported by MEC, grant MTM2016-75963-P. The second author has been supported by AICO/2016/30. The fourth author has been supported by MEC, grant MTM2015-65825-P.Conejero, JA.; Lizama, C.; Murillo-Arcila, M.; Seoane Sepúlveda, JB. (2019). 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Coexistence and optimal control problems for a degenerate predator-prey model

In this paper we present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered. \ua9 2010 Elsevier Inc

Smooth attractors of finite dimension for von Karman evolutions with nonlinear frictional damping localized in a boundary layer

In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the long-time behavior of nonlinear plates has been a topic of recent interest. Since the von Karman plate system is of "hyperbolic type" with critical nonlinearity (noncompact with respect to the phase space), this latter topic is particularly challenging in the case of geometrically constrained and nonlinear damping. In this paper we first show the existence of a compact global attractor for finite-energy solutions, and we then prove that the attractor is both smooth and finite dimensional. Thus, the hyperbolic-like flow is stabilized asymptotically to a smooth and finite dimensional set. Key terms: dynamical systems, long-time behavior, global attractors, nonlinear plates, nonlinear damping, localized dampin