Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies

We analyze long-time correlated Brownian motion and scaled Brownian motion on the surface of the two dimensional sphere $\mathbb{S}^{2}$. Due to the geometric effects induced by the $\mathbb{S}^{2}$ curvature, such correlations collude with specific dynamics (\emph{navigation strategies}) on the manifold topology to originate rich transport properties. We focus our study to two classes of navigation strategies: One induced by the specific set of coordinates chosen for $\mathbb{S}^2$ which defines a fixed frame of reference; in particular, we chose the basis induced by spherical coordinates. We find that contrary to what occurs in the absence of correlations non-equilibrium stationary distributions are attained. We elucidate an analogy of our results with those observed of fractional Brownian motion in confined by reflecting walls in one and two dimensions. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle as does the Frenet-Serret system, then the equilibrium uniform distribution on the sphere is attained. In both cases, the relaxation times towards the stationary distribution depend on the particular value of the Hurst parameter. We show that scaled Brownian motion on $\mathbb{S}^2$ is independent of the navigation strategy and we find a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on $\mathbb{S}^{2}$ and the numerical results obtained from our method to generate ensemble of trajectories.Comment: The statistics of Fractional Brownian motion and of scaled Brownian motion are analyzed when motion is constrained to surface of a spher

Dynamics of closed quantum systems under stochastic resetting

We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times between consecutive reset events. We analyse the behaviour of the state in the long-time regime, as well as the evolution of relevant quantities in the study of quantum coherence and closed- vs open-system dynamics. Our general results are complemented with examples involving paradigmatic resetting distributions, and special attention is paid to the two-level (qubit) system, in which we elucidate the effects of the renewal process on the speed of evolution toward an orthogonal state, and gain insight into the resetting applied to open systems.Comment: An analysis of closed quantum system subject to arbitrary stochastic resetting process is carried ou

The underlying order induced by orthogonality and the quantum speed limit

We perform a comprehensive analysis of the set of parameters $\{r_{i}\}$ that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time $\tau$, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between $\tau$ and the energy spectrum and allowing the classification of $\{r_{i}\}$ into families organized in a 2-simplex, $\delta^{2}$. Furthermore, the states determined by $\{r_{i}\}$ are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those $r_{i}$s in $\delta^{2}$ correspondent to states whose orthogonality time is limited by the Mandelstam--Tamm bound from those restricted by the Margolus--Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.Comment: orthogonality time; quantum speed limit; three-level systems; dynamics towards orthogonalit

The role of basic mathematics concepts in programming teaching and learning

App Inventor is an online tool to create apps for mobile devices with Android operating system. With this tool, teachers can develop applications and video games that help students to learn fundamental concepts of mathematics through programming. The implementation of the integer division algorithm firstly in App Inventor, and later in C++ using successive subtractions required a detailed explanation of this algorithm. We have implemented an algorithm that uses the integer division theorem in response to a problem detected among mathematics teachers interested in teaching programming. This study involved 19 participants in 4 institutions in Palmira and Medellín (Colombia). The results indicated that the programming languages such as C++, Java and Python presented the erroneous results in the integer division when the divisor is a negative number, a similar situation to that was observed among the participants who presented quotients and incorrect residues in most cases. Using App Inventor in a programming course with teachers Maths allowed us to enrich the application with a video game for the student’ self-evaluation in relation to the appropriation of the algorithm of the division of integer numbers

The rider behavior questionnaire to explore associations of motorcycle taxi crashes in Cartagena (Colombia)

Objective: This study aimed to identify the association between behavioral factors and crashes of motorcycle taxi riders using the Motorcycle Rider Behavior Questionnaire (MRBQ). Methods: This study was a cross-sectional survey of motorcycle taxi riders in Cartagena. The MRBQ was adapted to the socio-cultural context and contained 45 items. The survey was conducted between February 2019 and May 2019. The items of the MRBQ were processed using factor analysis. Four logistic regression models were used to analyze the association between behavioral factors and aspects of demographics, operating conditions, and experiencing nearcrashes, crashes, traffic tickets, and at-fault crashes. Results: Four hundred and thirty-eight motorcyclists participated. The exploratory factor analysis extracted five elements: stunts, speed violations, traffic errors, control errors, and safety, explaining 42% of the variance. The increase in riding per week showed significant differences with stunts, speed violations, and traffic errors. Riding experiences, traffic errors, control errors, and safety were significantly associated with crashes and near-crashes. Stunts were the strongest factors related to traffic tickets. Speed violations were the strongest factors associated with at-fault accidents. Conclusions: The study showed recent results considering behavioral, exposure, and operational conditions in a group of motorcycle taxi riders. The study recommends some practical implications for the well-being of motorcyclists and road safety

Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media

Applying evolution strategies to the optimization of fluid-solid interaction problems

Se investiga la utilidad de las Estrategias Evolutivas en la optimización de un problema que requiere el análisis por el método de elementos finitos de un sólido junto con un fluido en movimiento. El problema consiste en la minimización del peso de una lámina sujeta al paso del aire a través de un conducto cerrado. El problema presentado tiene el interés de ser multidisciplinario, con esquemas de integración y acoplamiento entre formulaciones muy distintas y con una extensión directa a problemas de ingeniería estructural, mecánica y aeronáutica.Peer Reviewe

Governance for Sustainability in an Organization in Central Mexico

Often, the total quality has been instrumented before being weighted. The strategies even precede a diagnosis in Mexican organizations, but in an opposite sense, the present work set out to establish the reliability and validity of an instrument to measure the perception of total quality based on three indicators related to management. , production and transfer of knowledge. A nonperimental study was carried out with a non-probabilistic selection of 124 administrative staff and employees from an organization in central Mexico. From a structural model ⌠X2 = 123,24 (23df) p = 0,010; GFI = 0,990; CFI =,991; IFI = 0,993; RMSEA = 0,007⌡, it was found that management affects production (0,38) and this about the total perceived quality (0,35), although there are lines of research concerning empathy, commitment, entrepreneurship, satisfaction and happiness in relation to the implementation of continuous improvements to the quality of processes and products