Mathematical Methods in the Physical Sciences

The erosion of bioerodible polymers depends on many factors including the polymer chain length, bond cleavage velocity, swellability, crystallinity, and water diffusivity in the polymer matrix. This multitude of parameters makes modeling of erosion difficult. Only a few models exist that describe morphological changes of polymers during erosion qualitatively. In the present approach the polymer matrix was represented as the sum of small individual polymer matrix parts. The factors that determine erosion were combined, and the erosion of each matrix piece was regarded as a random event. Once such a matrix piece had come into contact with water, an individual life expectation was assigned to it using Monte Carlo techniques. The proposed model can describe complicated phenomena such as changes in polymer matrix microstructure, movement of erosion fronts, creation of pores, and weight loss during erosion, yet it is simple and easy to use. For quantitative evaluations the model was fit to experimental data for weight loss and erosion front movement. The so obtained model constants proved to be useful for the prediction of independent parameters like the porosity of polymer matrices during erosion. This modeling approach may help broaden the understanding of the role of polymer erosion when considering bioerodible polymers in applications such as controlled drug delivery or tissue engineering.

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“…The expected value of C ( X i j ) is x. 19 Figure 3 shows an example for a grid n, = ny = 100 with x = 0.35.…”

Section: Configuring the Computational Grid Prior Tomentioning

confidence: 99%

Modeling of polymer erosion

Göpferich¹,

Langer²

1993

Macromolecules

167

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“…For a completely analytic analysis, the TH equations are transformed into (10). Use of the same procedure as that derived by Humi [19] makes (9) very simple,…”

Section: Vector [T X (T) T Y (T) T Z (T)]mentioning

confidence: 99%

“…Palmer [9] presented an elegant analytic solution for the problem by representing the continuous and variable thrust acceleration in a Fourier series with a period equal to the maneuver time. He used the Parseval's theorem [10] to make the infinite sum into a closed form. However, this analytic solution is limited to formation flying in only a circular or near-circular orbit because the HCW equations are used.…”

Section: Introductionmentioning

confidence: 99%

Analytic Solution for Fuel-Optimal Reconfiguration in Relative Motion

Cho

Park

2009

J Optim Theory Appl

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The current paper presents simple and general analytic solutions to the optimal reconfiguration of multiple satellites governed by a variety of linear dynamic equations. The calculus of variations is used to analytically find optimal trajectories and controls. Unlike what has been determined from previous research, the inverse of the fundamental matrix associated with the dynamic equations is not required for the general solution in the current study if a basic feature in the state equations is met. This feature is very common due to the fact that most relative motion equations are represented in the LVLH frame. The method suggested not only reduces the amount of calculations required, but also allows predicting the explicit form of optimal solutions in advance without having to solve the problem. It is illustrated that the optimal thrust vector is a function of the fundamental matrix of the given state equations, and other quantities, such as the cost function and the state vector during the reconfiguration, can be concisely represented as well. The analytic solutions developed in the current paper can be applied to most reconfiguration problems in linearized relative motions. Numerical simulations confirm the brevity and accuracy of the general analytic solutions developed in the current paper.

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“…Specifically it is required that they should be able to resist moisture and not degrade with UV heating nor with repeated heating or cooling. Generally silicone and acrylic are the most commonly used DEA materials 1 See [33] for derivation 6 as result of superior performance compared to the alternatives. However, acrylic does not possess the thermal stability and good frequency response [28] required for the present applications.…”

Section: Materials Selectionmentioning

confidence: 99%

Electro-active polymer (EAP) “dimple” actuators for flow control: Design and characterisation.

Dearing

Morrison

Iannucci

2010

Sensors and Actuators A: Physical

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The long-term goal of this work is the development of a 'smart' skin capable of sensing and real-time actuation of oncoming turbulent flow, specifically to reduce skin-friction drag. Active "dimples" are time-dependent depressions that optimally alter local flow conditions [2]. Lightweight Electro-Active Polymers (EAPs) are ideal for these control surfaces since they offer high strain rate, fast response, low power consumption and ease of manufacture [13]. Key features for integration into a control system are robustness and repeatable, predictable motion. For this objective dimples are assessed and values for out-of-plane deflection, frequency response and vibrational modes, failure modes as well as power consumption values are presented. The dimple design comprises a buckling actuator, which can actuate without the need of a directional bias, differentiating itself from previous designs [16,17,18,19,20,21]. It also actuates from flush to the surface providing asymmetrical forcing, a key consideration for flow control purposes. It is shown that the dimple actuates with vibrational modes higher than the fundamental, and that these are non-linear, an important consideration for this type of device. The power consumption of the device, as required for net power savings, and device robustness is promising.

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Mathematical Methods in the Physical Sciences

Cited by 99 publications

References 0 publications

Modeling of polymer erosion

Modeling of polymer erosion

Analytic Solution for Fuel-Optimal Reconfiguration in Relative Motion

Electro-active polymer (EAP) “dimple” actuators for flow control: Design and characterisation.

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