Removing zero Lyapunov exponents in volume-preserving flows

Baraviera and Bonatti proved that it is possible to perturb, in the c^1 topology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

The Nusselt numbers of horizontal convection

We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $\kappa$ is the molecular diffusivity of buoyancy $b$. This connection between $\mathbf{J}$ and $\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $\kappa\langle|\boldsymbol{\nabla} b|^2\rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent "surface Nusselt number", defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{\rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|\mathbf{\nabla}b|^2$ demanded by $\kappa\langle|\mathbf{\nabla}b|^2\rangle$.Comment: 16 pages, 7 figure

Critical thinking and its importance in the present days for social workers

Critical thinking is multidimensional, it encompasses the intellectual (logic, rationality), psychological (self-awareness, empathy), sociological (in terms of socio-historical context), ethics (norms and moral evaluation) and philosophical (meaning of nature and the human being). As a competency, or set of competencies, critical thinking can be developed and assessed. In this sense, the exploratory study that we intend to present aims to contribute to the evaluation of the importance that students attribute to critical thinking, as well as to the evaluation of critical thinking as a competence in the present situation. Before the pandemic situation we conducted a study with a universe of the 1st year social work students recently graduated, whose training included the critical thinking curricular unit in their study plan, we used as a data collection technician, a questionnaire with likert scale to measure the students opinions. The results were very positive and students admit that it helped them to analyze information (the importance of details), to practice curiosity and skepticism (to ask questions and compare with other sources) and to question (particularly, their own beliefs), including problem solving or decision making. With this recent challenge, consequence of Covid-19, it was necessary to alter all the previous model and adjust it to the pandemic situation through distance learning. Due to the characteristics of this curricular unit, we understand that in addition to the contents and usual dynamic, it was important to support students in adapting to the new methods and use this situation in favor of the benefits of thinking critically. Being a new situation for all (teachers and students) systematic evaluations were made to perceive if the results of the changes introduced were promoting the desired effect. Subsequently, in a total of 6 classes, with about 35 students each, we selected a non-probabilistic sample of 2 students of each class and each student was asked to make a critical assessment of the impact of this curricular unit in their learning process. Among other results that we intend to present, the key was to achieve a balance between the need for security and the need to know other ways of doing or thinking and classifying the critical thinking skills acquired as potentialities to support the uncertainty of the moment. This is where critical reflection (especially involving others) can play a key role in building trust by analyzing strengths-based practice, but it also allows considering alternative options, points of view, increase their ability to assess and position themselves in different contexts and learn to be prepared for unexpected situations.info:eu-repo/semantics/acceptedVersio

Possible Stellar Metallicity Enhancements from the Accretion of Planets

A number of recently discovered extrasolar planet candidates have surprisingly small orbits, which may indicate that considerable orbital migration takes place in protoplanetary systems. A natural consequence of orbital migration is for a series of planets to be accreted, destroyed, and then thoroughly mixed into the convective envelope of the central star. We study the ramifications of planet accretion for the final main sequence metallicity of the star. If maximum disk lifetimes are on the order of 10 Myr, stars with masses near 1 solar mass are predicted to have virtually no metallicity enhancement. On the other hand, early F and late A type stars with masses of 1.5--2.0 solar masses can experience significant metallicity enhancements due to their considerably smaller convection zones during the first 10 Myr of pre-main-sequence evolution. We show that the metallicities of an aggregate of unevolved F stars are consistent with an average star accreting about 2 Jupiter-mass planets from a protoplanetary disk having a 10 Myr dispersal time.Comment: 14 pages, AAS LaTeX, 3 figures, accepted to ApJ Letter