Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Evidence for a perception memory continuum: an EEG study in a healthy population

In line with current memory theories of a perception-memory continuum along the ventral visual pathway, there is evidence that the specific profile of enhanced memory in special populations (e.g. synaesthesia) is based on increased perceptual sensitivity. The main goal of this study was to test in a more general population, if increased perceptual sensitivity is indeed associated with enhanced memory performance. We measured ERPs in response to simple perceptual stimuli biasing either the ventral or the dorsal route and established if perceptual sensitivity in response to ventrally (but not dorsally) processed stimuli is associated with visual short term memory performance in a change detection task. Preliminary results confirm the hypothesis and strengthen the assumption of a perceptual-memory-continuum.

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Molecular Mechanics of Water Monomer

Simulation of the classical molecular dynamics of a water molecule can be useful in explaining normal modes of motion, Fourier Transforms, and fundamental frequencies of vibration, as illustrated herein.

El problema del continuum y sus implicancias en la teoría leibniziana de la sustancia

El problema del contínuum juega un papel decisivo en el desarrollo de la metafísica leibniciana de madurez. En los 70, dicho problema asomaba en sus intentos de explicar la naturaleza de la materia y la unión alma-cuerpo desde una perspectiva geométrico-mecanicista. Más tarde, la cuestión reaparece en la discusión con Arnauld sobre la unidad sustancial. Al hacer de la unidad real el criterio definitorio de la sustancia, Leibniz expulsa lo continuo al ámbito de lo ideal. Con este paso, su sistema se encamina hacia una ontología monadológica y hacia un esquema metafísico articulado en tres niveles (real, fenoménico e ideal).

El problema del continuum y sus implicancias en la teoría leibniziana de la sustancia

El problema del contínuum juega un papel decisivo en el desarrollo de la metafísica leibniciana de madurez. En los 70, dicho problema asomaba en sus intentos de explicar la naturaleza de la materia y la unión alma-cuerpo desde una perspectiva geométrico-mecanicista. Más tarde, la cuestión reaparece en la discusión con Arnauld sobre la unidad sustancial. Al hacer de la unidad real el criterio definitorio de la sustancia, Leibniz expulsa lo continuo al ámbito de lo ideal. Con este paso, su sistema se encamina hacia una ontología monadológica y hacia un esquema metafísico articulado en tres niveles (real, fenoménico e ideal).

El problema del continuum y sus implicancias en la teoría leibniziana de la sustancia

El problema del contínuum juega un papel decisivo en el desarrollo de la metafísica leibniciana de madurez. En los 70, dicho problema asomaba en sus intentos de explicar la naturaleza de la materia y la unión alma-cuerpo desde una perspectiva geométrico-mecanicista. Más tarde, la cuestión reaparece en la discusión con Arnauld sobre la unidad sustancial. Al hacer de la unidad real el criterio definitorio de la sustancia, Leibniz expulsa lo continuo al ámbito de lo ideal. Con este paso, su sistema se encamina hacia una ontología monadológica y hacia un esquema metafísico articulado en tres niveles (real, fenoménico e ideal).

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

Numerical analysis of axisymmetric shells by one-dimensional continuum elements suitable for high frequency excitations

Axisymmetric shells are analyzed by means of one-dimensional continuum elements by using the analogy between the bending of shells and the bending of beams on elastic foundation. The mathematical model is formulated in the frequency domain. Because the solution of the governing equations of vibration of beams are exact, the spatial discretization only depends on geometrical or material considerations. For some kind of situations, for example, for high frequency excitations, this approach may be more convenient than other conventional ones such as the finite element method.

Experimental and Analytical Study of Masonry Infill Reinforced Concrete Frames Retrofitted with Steel Braces

In the present work a seismic retrofitting technique is proposed for masonry infilled reinforced concrete frames based on the replacement of infill panels by K-bracing with vertical shear link. The performance of this technique is evaluated through experimental tests. A simplified numerical model for structural damage evaluation is also formulated according to the notions and principles of continuum damage mechanics. The proposed model is calibrated with the experimental results. The experimental results have shown an excellent energy dissipation capacity with the proposed technique. Likewise, the numerical predictions with the proposed model are in good agreement with experimental results.

Foundations and applications of non-equilibrium statistical mechanics

The full text of this article is available in the PDF provided.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

Self Learning and self evaluation exercises database in basic mechanics: a theoretical-practical approach

In the School of Mines of the Technical University of Madrid (UPM) the first course of different degrees has been implemented and adapted to the European Higher Educational Area (EHEA). In all of the degrees there is a first semester course which gathers all the contents of basic mechanics: from the first kinematics concepts to the rigid solid plane motion Before the Bologna process took place, the authors had established the final assessment of the theoretical contents through open questions of theoretical-practical character In the present work, the elaboration of a wide database containing theoretical-practical questions that students can access on line is presented. The questions are divided in thirteen different questionnaires composed of a number of questions randomly chosen from a certain group in the database. Each group corresponds to a certain learning objective that the student knows. After answering the questionnaire and checking the grade assigned according to the performance of the student, the pupils can see the correct response displayed on the screen and widely explained by the professors. This represents a 10% of the final grade. As the student can access the questionnaires as many times as they want, the main goal is the self-assessment of each learning objective and therefore, getting the students involved in their own learning process so they can decide how much time they need to acquire the required level.

A Damage Model for Masonry Infilled Frames

The effect of infill walls on the behaviour of frames is widely recognized, and, for several decades now, has been the subject of numerous experimental investigations. However, the analytical modeling of infilled panels and frames under in-plane loading is difficult and generally unreliable. From the point of view of the simulation technique the models may be divided into micromodels and simplified (or macro-) models. Based on the equivalent strut approach (simplified model), in this paper a damage model is proposed for the characterization of masonry walls submitted to lateral cyclic loads. The model, developed along the lines of the Continuum Damage Mechanics, have the advantages of including explicitly the coupling between damage and mechanical behaviour and so is consistent with the definition of damage as a phenomenon with mechanical consequences.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.