Case Of Small Perturbations Research Articles

Resonant Transitions Due to Changing Boundaries

The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (‘pantography’). The presence of resonant transitions involving the natural transition frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in depth, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.

A Dynamic Vector Model of Microstrip RF Resonators for High-Field MR Imaging

This paper describes a dynamic vector model for modelling the electromagnetic characteristics of microstrip radio-frequency (RF) resonators for high field magnetic resonance imaging (MRI). A biological tissue-equivalent load having a circular cross section is assumed in the analysis. The dynamic model uses the well-known Green's function for cylindrically stratified media to characterize all six components of the electromagnetic field excited by the microstrip lines. The accuracy of the method as a function of its parameters is assessed and the results compared with those obtained from the quasi-static method often used at low frequencies. The limits of the quasi-static assumption are investigated by comparing values for the modal propagation constant and the terminating capacitances required to tune the cavity resonance over a frequency range of 100 MHz-1 GHz. The dynamic method is further used to analyse the modal content of a microstrip head resonator. Finally, a variational approach is used to assess the impact of the intermodal coupling for the case of small perturbations in the shape and the position of the cylindrical phantom.

Dynamics of the Human Cervical Spine and Neuromuscular Control

AbstractThe influence of the neuromuscular control on the dynamics of the human cervical spine is investigated both experimentally and numerically within a long-term research addressed to the whiplash injury problem. First, the case of small perturbations along the sagittal plane is considered. Specific in vivo measurements highlight that the spinal behavior strictly depends on the muscular activity while contextual kineradiographic observations suggest that an approximate model for the neck could be implemented by considering an inverse pendulum scheme, if either ‘small’ extensions or ‘medium’ flexions are of concern. Although such a model is too simple to represent the complex spinal deformation during the whiplash event, it can still be used to address the study of some control issues. On this subject, specific numerical simulations show that the in vivo experiments could be reproduced by controlling this model via a delayed feedback. This is governed by the velocity of propagation of the action potent...

Substantiation of the Method of Density Functional in Classical and Quantum Statistical Mechanics

The relationship between a description of a multicomponent mixture based on the entropy functional with the terms quadratic in the density gradients of components and in the temperature on the one hand, and a description within the framework of classical and quantum statistical mechanics on the other hand, is investigated. Explicit expressions for the entropy functional are written in the context of classical and quantum theories. A quadratic approximation is then calculated for the case of small perturbations of a uniform state. The terms quadratic in the gradients are separated in this approximation. This allows ab initio calculations of the corresponding phenomenological coefficients to be done.

The study of the induction of subsonic wind tunnels with an axisymmetric working part

For the case of small perturbations of the velocity on the boundary of the flow and arbitrary degree of perforation of the wall of the wind tunnel which is constant along its length, a solution has been found for the axisymmetric boundary-value problem of subsonic flow around a thin body of revolution in perforated boundaries. The boundary condition connects the tangential component of the perturbed velocity and the component normal to the wall, and has a general form for the whole boundary. From the solution obtained, the optimum degree of perforation of the wall is found for which distortion of the pressure coefficient on the surface of the model is a minimum in comparison with the unbounded flow round the body. The questions of the induction of the walls of the working part of the wind tunnel, the formulation of the boundary condition, and the determination of the corrections to the aerodynamic characteristics of the model are considered in a number of studies [1–5]. Lately a promising method was been worked out for reducing the influence of the walls directly in the process of experiment by regulating the parameters of the gas near the boundary in such a way that they correspond to the parameters in flow round the same body by an unbounded flow [3, 5]. However, the design properties of many working tunnels do not permit this method to be applied. The induction of such tunnels as these can be reduced only by the choice of an optimum degree of perforation of the walls. In the articles [6–8] there is a study of the effect of perforated boundaries on the flow round a profile, the degree of perforation in [7] being assumed to be small.