One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Assessment of vascular invasion by bone and soft tissue tumours of the limbs: usefulness of MDCT angiography.

OBJECTIVE: To evaluate the accuracy of computed tomography angiography (CTA) in predicting arterial encasement by limb tumours, by comparing CTA with surgical findings (gold standard). METHODS: Preoperative CTA images of 55 arteries in 48 patients were assessed for arterial status: cross-sectional CTA images were scored as showing a fat plane between artery and tumour (score 0), slight contact between artery and tumour (score 1), partial arterial encasement (score 2) or total arterial encasement (score 3). Reformatted CTA images were assessed for arterial displacement, rigid wall, stenosis or occlusion. At surgery, arteries were classified as free or surgically encased; 45 arteries were free and 10 were surgically encased. RESULTS: Multivariate logistic regression identified the axial CTA score as a relevant predictor for arterial encasement and subsequent vascular intervention during surgery. All sites where CTA showed a fat plane between the tumour and the artery were classified as free at surgery (n = 28/28). The sensitivity of total arterial encasement on CTA (score 3) was 90%, specificity 93%, accuracy 93% and positive likelihood ratio 13.5. CONCLUSION: CTA evidence of total arterial encasement is a highly specific indication of arterial encasement. The presence of fat between the tumour and the artery on CTA rules out arterial involvement at surgery.

Peeling, healing and bursting in a lubricated elastic sheet

We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication and body forces. We then analyze various steady and unsteady problems for the sheet such as peeling, healing, levitating and bursting using a combination of numerical simulation and dimensional analysis. On the macro-scale, we corroborate our theory with a simple experiment, and on the micro-scale, we analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete pulses.

Basins of attraction changes by amplitude constraining of oscillators with limited power supply

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity. (c) 2005 Elsevier Ltd. All rights reserved.

Estudo da permeabilidade dos solos de fundação do aterro de resíduos sólidos urbanos de Bauru

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análisis del acoplamiento vibro-acústico en resonadores de membrana

El presente Trabajo Fin de Máster pretende llevar a cabo el análisis del comportamiento vibratorio de resonadores de membrana, consistentes en un panel delgado y ligero montado a cierta distancia de un elemento constructivo rígido y pesado. Este tipo de sistemas resonantes son empleados habitualmente como absorbentes de media-baja frecuencia en aplicaciones de acondicionamiento acústico de salas. El análisis hará especial hincapié en la influencia del acoplamiento mecánico-acústico entre la placa vibrante (estructura) y el colchón de aire (fluido) encerrado entre la misma y la pared rígida. En primer lugar, realizaremos el análisis modal experimental del resonador objeto de ensayo a partir de las mediciones de su respuesta vibratoria, con el fin de caracterizar su comportamiento en base a sus primeros modos propios acoplados de flexión. El análisis de las señales vibratorias en el dominio de la frecuencia para la identificación de dicho modos se realizará en el entorno de programación MATLAB, haciendo uso de una herramienta propia que implementa los métodos de cálculo y los algoritmos necesarios para tal fin. Asimismo, simularemos el comportamiento del resonador mediante el método de elementos finitos (FEM), utilizando las aplicaciones ANSYS y SYSNOISE, considerando diferentes condiciones frontera en el modelo generado. Los resultados aquí obtenidos serán de utilidad para complementar aquellos obtenidos de forma experimental a la hora de extraer conclusiones prácticas del análisis realizado. SUMMARY. This Master's Thesis intends to carry out the analysis of the vibratory behaviour of resonance absorbers, consisting of a thin and lightweight panel mounted at a distance from a rigid wall. Such systems are commonly used as sound absorption systems for mid-low frequency in room acoustics applications. The analysis will emphasize the influence of mechanical-acoustic coupling between the vibrating plate (structure) and the air cushion (acoustic element) enclosed behind it. First of all, we are performing the experimental modal analysis of the resonance absorber under test from the vibrational response measurements, in order to characterize its behaviour based on its first bending coupled-modes. The analysis of vibration signals in the frequency domain for the identification of such modes will be made in MATLAB programming environment, using a proprietary tool that implements the calculation methods and algorithms needed for this purpose. Furthermore, we are simulating the behaviour of the resonance absorber applying the Finite Element Method (FEM) – using ANSYS and SYSNOISE applications - considering different boundary conditions in the model created. The results from the simulation will be useful to complement those obtained experimentally when drawing practical conclusions from this analysis.

Contribuição ao estudo de treliças não lineares considerando efeitos térmicos

This work presents the numerical analysis of nonlinear trusses summited to thermomechanical actions with Finite Element Method (FEM). The proposed formulation is so-called positional FEM and it is based on the minimum potential energy theorem written according to nodal positions, instead of displacements. The study herein presented considers the effects of geometric and material nonlinearities. Related to dynamic problems, a comparison between different time integration algorithms is performed. The formulation is extended to impact problems between trusses and rigid wall, where the nodal positions are constrained considering nullpenetration condition. In addition, it is presented a thermodynamically consistent formulation, based on the first and second law of thermodynamics and the Helmholtz free-energy for analyzing dynamic problems of truss structures with thermoelastic and thermoplastic behavior. The numerical results of the proposed formulation are compared with examples found in the literature.

Sloshing and slamming oscillations in collapsible channel flow

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to an external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes contribute increasingly to the global instability and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.

Thoracic wall reconstruction using ultrasound images to model/bend the thoracic prosthesis for correction of pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior thoracic wall. The surgical correction of such deformity, using Nuss procedure, consists in the placement of a personalized convex prosthesis into sub-sternal position to correct the deformity. The aim of this work is the CT-scan substitution by ultrasound imaging for the pre-operative diagnosis and pre-modeling of the prosthesis, in order to avoid patient radiation exposure. To accomplish this, ultrasound images are acquired along an axial plane, followed by a rigid registration method to obtain the spatial transformation between subsequent images. These images are overlapped to reconstruct an axial plane equivalent to a CT-slice. A phantom was used to conduct preliminary experiments and the achieved results were compared with the corresponding CT-data, showing that the proposed methodology can be capable to create a valid approximation of the anterior thoracic wall, which can be used to model/bend the prosthesis

Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAs Project)

Background and purpose: Individual rupture risk assessment of intracranial aneurysms is a major issue in the clinical management of asymptomatic aneurysms. Aneurysm rupture occurs when wall tension exceeds the strength limit of the wall tissue. At present, aneurysmal wall mechanics are poorly understood and thus, risk assessment involving mechanical properties is inexistent. Aneurysm computational hemodynamics studies make the assumption of rigid walls, an arguable simplification. We therefore aim to assess mechanical properties of ruptured and unruptured intracranial aneurysms in order to provide the foundation for future patient-specific aneurysmal risk assessment. This work also challenges some of the currently held hypotheses in computational flow hemodynamics research. Methods: A specific conservation protocol was applied to aneurysmal tissues following clipping and resection in order to preserve their mechanical properties. Sixteen intracranial aneurysms (11 female, 5 male) underwent mechanical uniaxial stress tests under physiological conditions, temperature, and saline isotonic solution. These represented 11 unruptured and 5 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a 3-parameter (C(10), C(01), C(11)) Mooney-Rivlin hyperelastic model. Each aneurysm was classified according to its biomechanical properties and (un)rupture status.Results: Tissue testing demonstrated three main tissue classes: Soft, Rigid, and Intermediate. All unruptured aneurysms presented a more Rigid tissue than ruptured or pre-ruptured aneurysms within each gender subgroup. Wall thickness was not correlated to aneurysmal status (ruptured/unruptured). An Intermediate subgroup of unruptured aneurysms with softer tissue characteristic was identified and correlated with multiple documented risk factors of rupture. Conclusion: There is a significant modification in biomechanical properties between ruptured aneurysm, presenting a soft tissue and unruptured aneurysms, presenting a rigid material. This finding strongly supports the idea that a biomechanical risk factor based assessment should be utilized in the to improve the therapeutic decision making.

Wall motion estimation in intracranial aneurysms

The quantification of wall motion in cerebral aneurysms is becoming important owing to its potential connection to rupture, and as a way to incorporate the effects of vascular compliance in computational fluid dynamics (CFD) simulations.Most of papers report values obtained with experimental phantoms, simulated images, or animal models, but the information for real patients is limited. In this paper, we have combined non-rigid registration (IR) with signal processing techniques to measure pulsation in real patients from high frame rate digital subtraction angiography (DSA). We have obtained physiological meaningful waveforms with amplitudes in therange 0mm-0.3mm for a population of 18 patients including ruptured and unruptured aneurysms. Statistically significant differences in pulsation were found according to the rupture status, in agreement with differences in biomechanical properties reported in the literature.

A brief review and a new treatment for rigid bodies collision models

In general the motion of a body takes place in a confined environment and collision of the body with the containing wall is possible. In order to predict the dynamics of a body in this condition one must know what happens in a collision. Therefore, the problem is: if one knows the pre-collision dynamics of the body and the properties of the body and the wall one wants to predict the post-collision dynamics. This problem is quite old and it appeared in the literature in 1668. Up to 1984 it seemed that Newton's model was enough to solve the problem. But it was found that this was not the case and a renewed interest in the problem appeared. The aim of this paper is to treat the problem of plan collisions of rigid bodies, to classify the different models found in the literature and to present a new model that is a generalization of most of these models.

Dynamic earth pressures against a retaining wall caused by Rayleigh waves

An approximate procedure for studying harmonic soil-structure interaction problems is presented. The presence of Rayleigh waves is considered and the resulting governing equations of the dynamic soil-structure system are solved in the time domain. With this method the transient and steady states of a vibratory motion and also the nonlinear behaviour of the soil can be studied. As an example, the dynamic earth pressure against a rigid retaining wall is investigated. The loads are assumed to be harmonic Rayleigh waves with both static and dynamic surface surcharges. The dependence of the results on the excitation frequency is shown.

An analytical investigation into shear wall and slab interconnections between reinforced concrete modules for high -rise buildings utilising modular construction under extreme seismic and wind loading

This research investigates a new structural system utilising modular construction. Five-sided boxes are cast on-site and stacked together to form a building. An analytical model was created of a typical building in each of two different analysis programs utilising the finite element method (Robot Millennium and ETABS). The pros and cons of both Robot Millennium and ETABS are listed at several key stages in the development of an analytical model utilising this structural system. Robot Millennium was initially utilised but created an analytical model too large to be successfully run. The computation requirements were too large for conventional computers. Therefore Robot Millennium was abandoned in favour of ETABS, whose more simplistic algorithms and assumptions permitted running this large computation model. Tips are provided as well as pitfalls signalled throughout the process of modelling such complex buildings of this type. ^ The building under high seismic loading required a new horizontal shear mechanism. This dissertation has proposed to create a secondary floor that ties to the modular box through the use of gunwales, and roughened surfaces with epoxy coatings. In addition, vertical connections necessitated a new type of shear wall. These shear walls consisted of waffled external walls tied through both reinforcement and a secondary concrete pour. ^ This structural system has generated a new building which was found to be very rigid compared to a conventional structure. The proposed modular building exhibited a period of 1.27 seconds, which is about one-fifth of a conventional building. The maximum lateral drift occurs under seismic loading with a magnitude of 6.14 inches which is one-quarter of a conventional building's drift. The deflected shape and pattern of the interstorey drifts are consistent with those of a coupled shear wall building. In conclusion, the computer analysis indicate that this new structure exceeds current code requirements for both hurricane winds and high seismic loads, and concomitantly provides a shortened construction time with reduced funding. ^