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Sergio Rojas

Publications and source records attributed to Sergio Rojas.

26 records · Page 2Linked to original sources
arXiv2020

Adaptive stabilized finite elements: Continuation analysis of compaction banding in geomaterials

Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the capability of the material to diffuse internal perturbations and lead to localized failure features (e.g., cracks and compaction bands). This type of solution, generally found in fluids, has strong nonlinearities and periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, effective numerical tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This method provides a residual representation to drive adaptive mesh refinement, a particularly useful feature for the problem at hand. We compare against analytical and standard finite element solutions to demonstrate the performance of our approach. We then investigate the sensitivity of the diffusivity ratio, main parameter of the problem, and identify multiple possible solutions, with multiple stress peaks. Finally, we show the evolution of the spacing between peaks for all solutions as a function of that parameter.

physics.comp-ph↗
arXiv2019

An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that has inf-sup stability. We formulate this residual minimization as a stable saddle-point problem which delivers a stabilized discrete solution and a residual representation that drives the adaptive mesh refinement. Numerical results on an advection-reaction model problem show competitive error reduction rates when compared to discontinuous Galerkin methods on uniformly refined meshes and smooth solutions. Moreover, the technique leads to optimal decay rates for adaptive mesh refinement and solutions having sharp layers.

math.NA↗
arXiv2019

Residual minimization for isogeometric analysis in reduced and mixed forms

Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions for trial space results in excellent discrete approximations of the solution. However, we observe that high continuity for test spaces is not necessary. In this work, we present a framework which uses highly-continuous B-splines for the trial spaces and basis functions with minimal regularity and possibly lower order polynomials for the test spaces. To realize this goal, we adopt the residual minimization methodology. We pose the problem in a mixed formulation, which results in a system governing both the solution and a Riesz representation of the residual. We present various variational formulations which are variationally-stable and verify their equivalence numerically via numerical tests.

math.NA↗
arXiv2011

Enhancing Reasoning Skills in the Process of Teaching and Learning Physics via Dynamic Problem Solving Strategies: a Preparation for Future Learning

The large number of published articles in physics journals under the title "Comments on ..." and "Reply to ..." is indicative that the conceptual understanding of physical phenomena is very elusive and hard to grasp even to experts, but it has not stopped the development of Physics. In fact, from the history of the development of Physics one quickly becomes aware that, regardless of the state of conceptual understanding, without quantitative reasoning Physics would have not reached the state of development it has today. Correspondingly, quantitative reasoning and problem solving skills are a desirable outcomes from the process of teaching and learning of physics. Thus, supported by results from published research, we will show evidence that a well structured problem solving strategy taught as a dynamical process offers a feasible way for students to learn physics quantitatively and conceptually, while helping them to reach the state of an Adaptive Expert highly skillful on innovation and efficiency, a desired outcome from the perspective of a Preparation for Future Learning approach of the process of teaching and learning Physics effectively.

physics.gen-ph↗
arXiv2010

A non-standard approach to introduce simple harmonic motion

We'll be presenting an approach to solve the equation of simple harmonic motion (SHM) which is non-standard as compared with the usual way of solution presented in textbooks. In addition to help students avoid the unnecessary memorization of formulas to solve physics problems, this approach could help instructors to present the subject in a teaching framework which integrates conceptual and mathematical reasoning, in a systemic way of thinking that will help students to reinforce their quantitative reasoning skills by using mathematical knowledge already familiar to students in a first calculus-based introductory physics course, such as the chain rule for derivatives, inverse trigonometric functions, and integration methods.

physics.ed-ph↗
arXiv2010

Continuous opinion model in small world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance $ε$. In directed networks, if agent i is a neighbor of agent j, j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions $ $ and their distribution as a function of $ε$ and of the network structural disorder. In directed networks $ $ exhibits a rich structure, being larger than in undirected networks for higher values of $ε$, and smaller for lower values of $ε$.

physics.soc-ph↗
arXiv2009

On the teaching and learning of physics: A Criticism and a Systemic Approach

The amount of published research in Physics Education Research (PER) shows, on one hand, an increasing interest in the design and development of high performance physics teaching strategies, and, on the other hand, it tries to understand plausible ways on which the brain processes scientific information so that scientific thinking skills could be taught more effectively. As physics is a subject in which mathematical and conceptual reasoning can not be separated, instructors of physics face the problem of finding suitable advise on the most effective methods of teaching physics (i.e. how much time should be spent on intuitive conceptual reasoning and how much time in developing quantitative reasoning, and how to teach both in a unitary way). In spite the important efforts made by the PER community, the published results are overwhelming and confusing for the physics instructors in the sense that the conclusions that have arisen in those articles are in some instances controversial and far from being conclusive in pointing out a particular strategy to overcome the afore mentioned problem. Accordingly, based on the analysis of published PER work, we'll be arguing that one of the major difficulties to overcome in the teaching of physics could be associated to the lack of a consistent and coherent methodological framework for teaching which integrates both aspects, conceptual and mathematical reasoning, in a systemic way of thinking. We will be presenting a set of plausible steps that could be applied to tackle the aforementioned difficulty.

physics.ed-ph↗