Dynamics of linear polymers in random media

We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian dynamics and estimate the diffusion constant of the center-of-mass of the chain in such disordered media. For internal dynamics of the chain, we estimate the dynamic exponents. We propose similar scaling theory for the reptation dynamics of the chain in the framework of Flory theory for the disordered medium. The modifications in the case of correlated disordered are also discussed.Comment: 4 pages, no figure

La habilidad argumentativa escrita a través del aprendizaje del concepto reactivo límite mediante el uso de prácticas de laboratorio

El propósito de este trabajo es presentar los resultados obtenidos en la investigación que busca desarrollar la Habilidad Argumentativa a través del aprendizaje del concepto reactivo limite, mediante el uso de las prácticas de laboratorio con estudiantes de grado decimo (10°). En la investigación se busca mostrar el desarrollo de la Habilidad Argumentativa y la Argumentación como categoría relevante del pensamiento crítico, a través de la formulación, planeación, diseño y aplicación de la unidad didáctica en química inorgánica. En ese sentido se diseñó e implemento una unidad didáctica acerca del concepto de reactivo límite que sirve como complemento para la enseñanza del tema (reactivo límite) general de estequiometria en el grado decimo de la Institución Educativa Arenys de Mar de la ciudad de Medellín. La investigación emprendida es de carácter cualitativo en la cual se estudian los procesos argumentativos en química inorgánica aplicado a un grupo conformado por 28 estudiantes donde se toma una muestra de 6 estudiantes; los estudiantes seleccionados para la unidad de trabajo, fueron determinados en el marco de su rendimiento académico entorno a los resultados arrojados por el resumen de evaluación de los periodos academismos cursados por los mismos. Esta investigación toma como base el modelo argumentativo de Toulmin y con el grupo de estudiantes objetos de estudio, se realiza la exploración de ideas previas para tomar conciencia y ajustar la unidad didáctica en torno de los posibles obstáculos con los que cuentan los estudiantes en términos de aprendizaje; posterior a la exploración de ideas previas se aplica un diagnóstico inicial y un diagnóstico final; se analizan los resultados para determinar el nivel de la Habilidad Argumentativa con la que cuentan los estudiantes y así categorizarlos en 3 grupos (Alto, Medio, Bajo). Los resultados analizados se hacen entorno al modelo argumentativo de Jiménez Aleixandre y Díaz de Bustamante (2003) y para la calidad del argumento se toma a Marín (2018). Por otra parte, se pudo establecer que una vez se emprendió y desarrollo la intervención didáctica, los estudiantes lograron una mejor tendencia en su Habilidad Argumentativa mejorando de un nivel bajo a medio e incluso algunos estudiantes alcanzaron el nivel alto tanto en Habilidad Argumentativa como en la calidad los argumentos.The purpose of this work is to present the results obtained in the research that seeks to develop the Argumentative Skill through the learning of the limit reactive concept, through the use of laboratory practices with 10th grade students. The research seeks to show the development of Argumentative Skill and Argumentation as a relevant category of critical thinking, through the formulation, planning, design and application of the didactic unit in inorganic chemistry. In that sense, a didactic unit was designed and implemented on the concept of the limit reagent that serves as a complement to the teaching of the general topic (limit reagent) of stoichiometry in the tenth grade of the Arenys de Mar Educational Institution of the city of Medellín. The research undertaken is qualitative in which the argumentative processes in inorganic chemistry applied to a group consisting of 28 students are studied, where a sample of 6 students is taken; The students selected for the work unit were determined within the framework of their academic performance based on the results obtained by the evaluation summary of the academic periods studied by them. This research is based on Toulmin's argumentative model and with the group of students objects of study, the exploration of previous ideas is made to raise awareness and adjust the teaching unit around the possible obstacles that students have in terms of learning; after the exploration of previous ideas an initial diagnosis and a final diagnosis are applied; The results are analyzed to determine the level of Argumentative Skill that students have and thus categorize them into 3 groups (High, Medium, Low). The analyzed results are based on the argumentative model of Jiménez Aleixandre and Díaz de Bustamante (2003) and for the quality of the argument, Marín (2018) is taken. On the other hand, it was established that once the didactic intervention was undertaken and developed, the students achieved a better tendency in their Argumentative Skill by improving from a low to medium level and even some students reached the high level both in Argumentative Skill and in the Quality arguments

Polymers and manifolds in static random flows: a renormalization group study

We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for directed polymers (each monomer sees a different flow) and for d < 6 for isotropic polymers (each monomer sees the same flow) and more generally for d<d_c(D) in the case of a manifold. This leads to new large scale behavior, which we analyze using field theoretical methods. We show that all divergences can be absorbed in multilocal counter-terms which we compute to one loop order. We obtain the non trivial roughness zeta, dynamical z and transport exponents phi in a dimensional expansion. For directed polymers we find zeta about 0.63 (d=3), zeta about 0.8 (d=2) and for isotropic polymers zeta about 0.8 (d=3). In all cases z>2 and the velocity versus applied force characteristics is sublinear, i.e. at small forces v(f) f^phi with phi > 1. It indicates that this new state is glassy, with dynamically generated barriers leading to trapping, even by a divergenceless (transversal) flow. For random flows with long-range (LR) correlations, we find continuously varying exponents with the ratio gL/gT of potential to transversal disorder, and interesting crossover phenomena between LR and SR behavior. For isotropic polymers new effects (e.g. a sign change of zeta - zeta_0) result from the competition between localization and stretching by the flow. In contrast to purely potential disorder, where the dynamics gets frozen, here the dynamical exponent z is not much larger than 2, making it easily accessible by simulations. The phenomenon of pinning by transversal disorder is further demonstrated using a two monomer ``dumbbell'' toy model.Comment: Final version, some explications added and misprints corrected (69 pages latex, 40 eps-figures included

Statistics of self-avoiding walks on randomly diluted lattice

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.Comment: 34 pages (+ 12 figures), REVTEX 3.

A Feasibility Study for Recycling Used Automotive Oil Filters In A Blast Furnace

This feasibility study has indicated that of the approximately 120,000 tons of steel available to be recycled from used oil filters (UOF's), a maximum blast furnace charge of 2% of the burden may be anticipated for short term use of a few months. The oil contained in the most readily processed UOF's being properly hot drained and crushed is approximately 12% to 14% by weight. This oil will be pyrolized at a rate of 98% resulting in additional fuel gas of 68% and a condensable hydrocarbon fraction of 30%, with the remaining 2% resulting as carbon being added into the burden. Based upon the writer's collected information and assessment, there appears to be no operational problems relating to the recycling of UOF's to the blast furnace. One steel plant in the US has been routinely charging UOF's at about 100 tons to 200 tons per month for many years. Extensive analysis and calculations appear to indicate no toxic consideration as a result of the pyrolysis of the small contained oil ( in the 'prepared' UOFs) within the blast furnace. However, a hydrocarbon condensate in the ''gasoline'' fraction will condense in the blast furnace scrubber water and may require additional processing the water treatment system to remove benzene and toluene from the condensate. Used oil filters represent an additional source of high quality iron units that may be effectively added to the charge of a blast furnace for beneficial value to the operator and to the removal of this resource from landfills

Directed polymer – directed percolation transition: the strong disorder case

The transition of physical properties in disordered systems from strong disorder characteristics to weak disorder characteristics is studied for the directed polymer case. It is shown analytically that this transition is governed by the ratio ρ(pc)/k, where ρ is the probability density of the maximal bond of the optimal Min-Max path, pc is the critical probability of directed percolation, and k is the degree of disorder. This analytic result is found to be in agreement with numerical results related to this transition. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005