Mean square displacement for a discrete centroid model of cell motion

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

Rotational self-friction problem of elastic rods

The aim of this paper is to extend the modeling of a hyperelastic rod undergoing large displacements with tangential self-friction to their modeling with rotational self-friction. As well as the discontinuity of contact force into a contact region not known in advance, taking into account the effects of friction in this problem type underlies more serious modeling, mathematical and numerical analysis difficulties. In this paper, we present an accurate modeling of rotational and tangential self-friction with Coulomb's law and also describe an augmented Lagrangian method to present a weak variational formulation approach of this problem. We then use the minimization method of the total energy to present an existence result of solution for the nonlinear penalized formulation. Finally, we give the linearization and the finite-element discretization of the weak variational formulation that can be useful for a numerical implementation.

3-Bit Digital-to-Analog Converter with Mechanical Amplifier for Binary Encoded Large Displacements

We present the design, fabrication, and characterization of a MEMS-based 3-bit Digital-to-Analog Converter (DAC) that allows the generation of large displacements. The DAC consists of electrostatic bending-plate actuators that are connected to a mechanical amplifier (mechAMP), enabling the amplification of the DAC output displacement. Based on a parallel binary-encoded voltage signal, the output displacement of the system can be controlled in an arbitrary order. Considering the system design, we present a simplified analytic model, which was confirmed by FE simulation results. The fabricated systems showed a total stroke of approx. 149.5 ± 0.3 µm and a linear stepwise displacement of 3 bit correlated to 23 ≙ eight defined positions at a control voltage of 60 V. The minimum switching time between two input binary states is 0.1 ms. We present the experimental characterization of the system and the DAC and derive the influence of the mechAMP on the functionality of the DAC. Furthermore, the resonant behavior and the switching speed of the system are analyzed. By changing the electrode activation sequence, 27 defined positions are achieved upgrading the 3-bit systems into a 3-tri-state (33) system.

Assessment of Geometric Nonlinearities Influence On NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Numerical study on trajectory of released store with manipulation of grid connections

Purpose This study aims to present a moving grid method based on the manipulation of connections. Design/methodology/approach In this study, the grid’s connections were manipulated to simulate a released store’s displacement. The selected model in this research is the EGLIN test case. In the introduced method, connections are modified in specific nodes of the grid. Governing flow equations were solved with the finite volume method. The major characteristic of this technique is using the averaging method for calculating the flux of cells. Findings This method maintains the grid’s quality even in large displacements of the released store. The three-dimensional simulation was carried out in transonic and supersonic regimes. Comparison of the results with experimental data were highly satisfactory. Research limitations/implications Using this moving grid method is recommended for simulating other models. Practical implications Prediction of store trajectory released from air vehicles is one of the most critical issues under study especially in the design of new stores. Originality/value The most prominent advantage of this method is maintaining the grid quality simultaneous with large displacements of the released store.

Assessment of Geometric Nonlinearities Influence on NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote re-producibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.