Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical dat

Calculation of the statistical properties in intermittency using the natural invariant density

We use the natural invariant density of the map and the Perron–Frobenius operator to analytically evaluate the statistical properties for chaotic intermittency. This study can be understood as an improvement of the previous ones because it does not introduce assumptions about the reinjection probability density function in the laminar interval or the map density at pre-reinjection points. To validate the new theoretical equations, we study a symmetric map and a non-symmetric one. The cusp map has symmetry about x = 0, but the Manneville map has no symmetry. We carry out several comparisons between the theoretical equations here presented, the M function methodology, the classical theory of intermittency, and numerical data. The new theoretical equations show more accuracy than those calculated with other techniques.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: del Río, Ezequiel. Universidad Politécnica de Madrid; EspañaFil: Lorenzon, Denis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentin

Intermittency reinjection in the logistic map

Just below a Period-3 window, the logistic map exhibits intermittency. Then, the third iterate of this map has been widely used to explain the chaotic intermittency concept. Much attention has been paid to describing the behavior around the vanished fixed points, the tangent bifurcation, and the formation of the characteristic channel between the map and the diagonal for type-I intermittency. However, the reinjection mechanism has not been deeply analyzed. In this paper, we studied the reinjection processes for the three fixed points around which intermittency is generated. We calculated the reinjection probability density function, the probability density of the laminar lengths, and the characteristic relation. We found that the reinjection mechanisms have broader behavior than the usually used uniform reinjection. Furthermore, the reinjection processes depend on the fixed point.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: del Río, Ezequiel. Escuela Tecnica Superior de Ingenieros Aeronauticos; España. Universidad Politécnica de Madrid; EspañaFil: Elaskar, Silvina Azul. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas; Argentin

Characteristic relation in Type-II intermittency

Intermitencia es una ruta hacia caos donde soluciones de sistemas dinámicos muestran alternancia entre comportamientos regulares (o laminares) y caóticos (o fases no regulares). Las fases laminares se corresponden con zonas de pseudo-equilibrio y/o soluciones pseudo-periódicas. En mecánica de fluidos el fenómeno de intermitencia tiene un importante papel en flujos turbulentos. En este trabajo se analiza la relación característica en intermitencia tipo-II cuando la función probabilidad de reinyección es uniforme. Tradicionalmente se han propuesto dos relaciones características en las cuales el parámetro de control aparece elevado a -1/2 y a -1 respectivamente. Se estudia bajo que condiciones cada una de las relaciones es correcta. Los resultados teóricos propuestos se verifican mediante simulaciones numéricas mostrando una elevada concordancia.Intermittency is a route to chaos where the dynamical system solutions show alternation between regular (or laminar) and chaotic (or non-regular) behaviors. The laminar phases correspond to pseudo-equilibrium zones and/or pseudo-periodic solutions. In fluid mechanics, the intermittency phenomenon plays an important role in turbulent flows. In this paper, the characteristic relation for type-II intermittency is analyzed when the reinjection probability function is uniform. Traditionally, two characteristic relations have been proposed in which the control parameter appears elevated to -1/2 and -1 respectively. In this paper under what conditions each of the relations is correct is studied. The proposed theoretical results are verified by numerical simulations showing high accuracy.Fil: Elaskar, Sergio Amado. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: Lorenzon, Denis. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Del Río, Ezequiel. Universidad Politécnica de Madrid; Españ

The fourth state of matter? Plasma introduction for pre-university studies

El plasma es un gran desconocido en los estudios de física a nivel preuniversitario ya que no se incluye explícitamente en los temarios de ninguna asignatura de ciencias. Sin embargo, su presencia en la naturaleza y en dispositivos de uso cotidiano es habitual, de forma que su estudio puede resultar apropiado para fomentar la motivación del alumnado hacia la física. En el presente artículo se describe una breve propuesta para introducir este concepto a los estudiantes de física de Educación Secundaria y Bachillerato. Este trabajo propone una introducción enmarcada en la perspectiva de las relaciones Ciencia-Tecnología-Sociedad-Ambiente (CTSA), una posterior discusión teórica donde se presentan los conceptos básicos que caracterizan un plasma y, por último, un sencillo experimento que muestra cómo un tubo fluorescente convencional contiene un plasma. Se pretende, con dicha propuesta, introducir el concepto de plasma a los estudiantes, así como fomentar su interés por la tecnología y ciencia que nos rodea en el día a día, de forma que permita al alumno contextualizar sus estudios de física, mediante un primer acercamiento a un campo multidisciplinar como es la física de plasmas.Plasma is not a well-known topic in pre-university courses since, in general, it is not included in the syllabus of any science subject. However, plasma is present in nature and in everyday usage devices, being its study appropriate to make the students be more motivated to study physics. This paper presents a short proposal in order to introduce this concept to High-School students of physics. This work begins with an introduction based on a Science-Technology-Society-Environment (STSE) perspective, followed by a theoretical discussion to describe the basic concepts of a plasma. Finally, a simple experiment is described to show that a common fluorescent lamp contains a plasma. In pursuance of this proposal, we wish to introduce the plasma concept to the students as well as to promote their interest on the daily life technology and science, allowing the students to contextualize their physics studies thanks to a first approach to a multidisciplinar subject as the physics of plasma

¿El cuarto estado de la materia? Introducción al plasma para estudios pre-universitarios

Plasma is not a well-known topic in pre-university courses since, in general, it is not included in the syllabus of any science subject. However, plasma is present in nature and in everyday usage devices, being its study appropriate to make the students be more motivated to study physics. This paper presents a short proposal in order to introduce this concept to High-School students of physics. This work begins with an introduction based on a Science-Technology-Society-Environment (STSE) perspective, followed by a theoretical discussion to des-cribe the basic concepts of a plasma. Finally, a simple experiment is described to show that a common fluores-cent lamp contains a plasma. In pursuance of this proposal, we wish to introduce the plasma concept to the stu-dents as well as to promote their interest on the daily life technology and science, allowing the students to con-textualize their physics studies thanks to a first approach to a multidisciplinar subject as the physics of plasma.El plasma es un gran desconocido en los estudios de física a nivel preuniversitario ya que no se incluye explícitamente en los temarios de ninguna asignatura de ciencias. Sin embargo, su presencia en la naturaleza y en dispositivos de uso cotidiano es habitual, de forma que su estudio puede resultar apropiado para fomentar la motivación del alumnado hacia la física. En el presente artículo se describe una breve propuesta para introducir este concepto a los estudiantes de física de Educación Secundaria y Bachillerato. Este trabajo propone una introducción enmarcada en la perspectiva de las relaciones Ciencia-Tecnología-Sociedad-Ambiente (CTSA), una posterior discusión teórica donde se presentan los conceptos básicos que caracterizan un plasma y, por último, un sencillo experimento que muestra cómo un tubo fluorescente convencional contiene un plasma. Se pretende, con dicha propuesta, introducir el concepto de plasma a los estudiantes, así como fomentar su interés por la tecnología y ciencia que nos rodea en el día a día, de forma que permita al alumno contextualizar sus estudios de física, mediante un primer acercamiento a un campo multidisciplinar como es la física de plasmas.Palabras clave: Física de plasmas; Ciencia-Tecnología-Sociedad-Ambiente (CTSA); Multidisciplinariedad; Práctica de laboratorio; Unidad didáctica.The fourth state of matter? Plasma introduction for pre-university studiesPlasma is not a well-known topic in pre-university courses since, in general, it is not included in the syllabus of any science subject. However, plasma is present in nature and in everyday usage devices, being its study appropriate to make the students be more motivated to study physics. This paper presents a short proposal in order to introduce this concept to High-School students of physics. This work begins with an introduction based on a Science-Technology-Society-Environment (STSE) perspective, followed by a theoretical discussion to describe the basic concepts of a plasma. Finally, a simple experiment is described to show that a common fluorescent lamp contains a plasma. In pursuance of this proposal, we wish to introduce the plasma concept to the students as well as to promote their interest on the daily life technology and science, allowing the students to contextualize their physics studies thanks to a first approach to a multidisciplinar subject as the physics of plasma.Keywords: Plasma physics; Science-Technology-Society-Environment (STSE); Multidisciplinarity; Laboratory experiment; Didactical sequence

Aprendizajes y prácticas educativas en las actuales condiciones de época: COVID-19

“Esta obra colectiva es el resultado de una convocatoria a docentes, investigadores y profesionales del campo pedagógico a visibilizar procesos investigativos y prácticas educativas situadas en el marco de COVI-19. La misma se inscribe en el trabajo llevado a cabo por el equipo de Investigación responsable del Proyecto “Sentidos y significados acerca de aprender en las actuales condiciones de época: un estudio con docentes y estudiantes de la educación secundarias en la ciudad de Córdoba” de la Facultad de Filosofía y Humanidades. Universidad Nacional de Córdoba. El momento excepcional que estamos atravesando, pero que también nos atraviesa, ha modificado la percepción temporal a punto tal que habitamos un tiempo acelerado y angustiante que nos exige la producción de conocimiento provisorio. La presente publicación surge como un espacio para detenernos a documentar lo que nos acontece y, a su vez, como oportunidad para atesorar y resguardar las experiencias educativas que hemos construido, inventado y reinventando en este contexto. En ella encontrarán pluralidad de voces acerca de enseñar y aprender durante la pandemia. Este texto es una pausa para reflexionar sobre el hacer y las prácticas educativas por venir”.Fil: Beltramino, Lucia (comp.). Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Escuela de Archivología; Argentina

New generalization for the intermittency theory for type I, II and III

Fil: Del Río, Ezequiel. Universidad Politécnica de Madrid; España.Fil: Elaskar, Sergio A. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina.Fil: Elaskar, Sergio A. Universidad Nacional de Córdoba. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaThe concept of intermittency has been introduced by Pomeau and Maneville in the context of the Lorenz system and are usually classified in three classes called I, II, and III. Intermittency is a specific route to the deterministic chaos when spontaneous transitions between laminar and chaotic dynamics occur.Fil: Del Río, Ezequiel. Universidad Politécnica de Madrid; España.Fil: Elaskar, Sergio A. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina.Fil: Elaskar, Sergio A. Universidad Nacional de Córdoba. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaMatemática Aplicad

New advances on chaotic intermittency and its applications

One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data. As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittency type, is now a function depending on the whole map, not just on the local map. Also, a new analytical approach to obtain the RPD from the mathematical expression of the map is presented. In this way all cases of non standard intermittencies are included in the same frame work. This methodology is extended to evaluate the noisy reinjection probability density function (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. This is an important difference with respect to the classical approach based on the Fokker-Plank equation or Renormalization Group theory, where the noise effect was usually considered just on the local Poincaré map. Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. Along the book examples of applications are described, which have shown very good agreement with numerical computations.

Review of Chaotic Intermittency

Chaotic intermittency is characterized by a signal that alternates aleatory between long regular (pseudo-laminar) phases and irregular bursts (pseudo-turbulent or chaotic phases). This phenomenon has been found in physics, chemistry, engineering, medicine, neuroscience, economy, etc. As a control parameter increases, the number of chaotic phases also increases. Therefore, intermittency presents a continuous route from regular behavior to chaotic motion. In this paper, a review of different types of intermittency is carried out. In addition, the description of two recent formulations to evaluate the reinjection processes is developed. The new theoretical formulations have allowed us to explain several tests previously called pathological. The theoretical background also includes the noise effects in the reinjection mechanism