Uniformity is weaker than semi-uniformity for some membrane systems

We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples of such models include Boolean circuits, membrane systems, DNA computers, chemical reaction networks and tile assembly systems, and there are many others. However, in such models there are actually two distinct kinds of uniformity condition. The first is the most common and well-understood, where each input length is mapped to a single computing device (e.g. a Boolean circuit) that computes on the finite set of inputs of that length. The second, called semi-uniformity, is where each input is mapped to a computing device for that input (e.g. a circuit with the input encoded as constants). The former notion is well-known and used in Boolean circuit complexity, while the latter notion is frequently found in literature on nature-inspired computation from the past 20 years or so. Are these two notions distinct? For many models it has been found that these notions are in fact the same, in the sense that the choice of uniformity or semi-uniformity leads to characterisations of the same complexity classes. In other related work, we showed that these notions are actually distinct for certain classes of Boolean circuits. Here, we give analogous results for membrane systems by showing that certain classes of uniform membrane systems are strictly weaker than the analogous semi-uniform classes. This solves a known open problem in the theory of membrane systems. We then go on to present results towards characterising the power of these semi-uniform and uniform membrane models in terms of NL and languages reducible to the unary languages in NL, respectively.Comment: 28 pages, 1 figur

Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and restricted evolution rules only. We show that every problem in P can be solved with uniform families of any of these variants. This, using known results on the upper bound of the computational power of variants (1) and (3) yields new characterizations of the class P. In the case of variant (2) we provide a further characterization of P by giving a semantic restriction on the computations of P systems of this varian

Evaluating space measures in P systems

P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented

Characterising the complexity of tissue P systems with fission rules

We analyse the computational efficiency of tissue P systems, a biologically-inspired computing device modelling the communication between cells. In particular, we focus on tissue P systems with fission rules (cell division and/or cell separation), where the number of cells can increase exponentially during the computation. We prove that the complexity class characterised by these devices in polynomial time is exactly P^#P, the class of problems solved by polynomial-time Turing machines with oracles for counting problems

Space complexity equivalence of P systems with active membranes and Turing machines

We prove that arbitrary single-tape Turing machines can be simulated by uniform families of P systems with active membranes with a cubic slowdown and quadratic space overhead. This result is the culmination of a series of previous partial results, finally establishing the equivalence (up to a polynomial) of many space complexity classes defined in terms of P systems and Turing machines. The equivalence we obtained also allows a number of classic computational complexity theorems, such as Savitch's theorem and the space hierarchy theorem, to be directly translated into statements about membrane systems

Modelling and prediction of non-linear scale-up from an Ultra Scale-Down membrane device to process scale tangential flow filtration

Ultra scale-down (USD) tools have demonstrated the huge potential for accelerated process development by significantly reducing the material requirements and providing better solutions, as part of the Quality by Design initiative. Key benefits of using USD techniques include the relatively small quantities of feedstock and minimal capital equipment needed to generate large volumes of statistically significant process data in a short period, leading to significant time and cost savings during process development. However, the use of small scale devices such as the stirred cell filtration units have been primarily limited to preliminary testing and initial screening due to their geometric and flow dissimilarities to tangential flow filtration at scale. As a result, process development and optimisation trials are generally carried out using the smallest c commercially available TFF cassettes, the use of which are primarily limited by time and material constraints that are invariably present at the early stages of process development. Therefore, the central focus of this work was to develop a USD methodology and model to accurately predict the performance of large scale tangential flow filtration (TFF) using a USD membrane filtration device. // The commercial package COMSOL was used to carry out computational fluid dynamics (CFD) modelling and simulation of the fluid flow dynamics in Pellicon TFF cassettes with different feed screens and a USD membrane device, in order to develop average wall shear rate correlations and channel pressure drops expressed as functions of the respective hydrodynamic conditions across scales. In addition, the impact of non-TFF related factors such as the system and cassette-specific hydraulic resistances on TFF performance was characterised using semi-empirical models. Finally, a scale-up methodology and mathematical model to predict the large scale performance using USD data was developed by combining the various resistances, channel pressure drop correlations and an empirical USD-derived model that characterises the specific feed-membrane interactions. The CFD simulations were independently verified using 2D particle imaging velocimetry to compare experimental data to the CFD simulated data. // 100-fold scale-up experiments were carried out based on equivalent averaged wall shear rates (w) as the geometry-independent parameter. Permeate flux excursions were carried out to validate the USD methodology and prediction model, by comparing USD model predictions against the large scale experimental data. Different membranes, feed screens (A, C and V) and feedstock, ranging from simple proteins like Bovine Serum Albumin (BSA) to more complex, multicomponent feed such as Escherichia coli homogenate, were used. Predicted flux and transmission results were in good agreement with the large scale experimental data, showing less than 5% difference across scales, demonstrating the robustness of the non-linear scale-up model. // Following the successful validation of the scale-up methodology and prediction model, other potential applications of the USD membrane device such as the optimisation of TFF microfiltration was demonstrated using Saccharomyces cerevisae and Chlorella sorokiniana. Fed-batch concentration experiments using Saccharomyces cerevisae were done to compare the volumetric throughput limits. The USD-predicted capacity limit of 49.2 L/m2 was very similar to the experimental large scale capacity value of 52.0 L/m2, and considered fully scalable within experimental errors. Finally, fouling studies were performed using Chlorella sorokiniana and the USD device to investigate the impact of media type and growth conditions on the filtration performance. The results indicated a strong correlation between soluble fouling species, such as exopolysaccharides and carbohydrates, rather than the algal biomass. A novel, dynamic flux control methodology was developed based on empirically determined critical fluxes expressed as a function of cell concentration. The dynamic control strategy was successfully verified by performing a 50-fold concentration experiment using a hollow fibre module and the USD device. An improvement of greater than 50% in average throughput was achieved using the 3-step flux cascade compared to the traditional flux-time/capacity optimised fluxes, with no observable increase in TMP throughout. // The work presented here demonstrates the potential of ultra scale-down tools coupled with a mathematical modelling approach to establish a predictable scale-up performance, which can be used to rapidly develop and optimise tangential flow filtration processes, regardless of differences in geometry, flow configuration and system setup

Optimization of permeable membrane microchannel heat sinks for additive manufacturing

The design freedom brought by additive manufacturing (AM) can be leveraged in the design of microchannel heat sinks to improve their cooling performance. The permeable membrane microchannel (PMM) heat sink geometry was inspired by the ability of powder bed AM processes to fabricate partially porous metal parts having small internal flow features on the order of the powder size. The design routes coolant through a parallel array of thin permeable membranes arranged in a single-layer-manifold configuration. The permeable membranes provide effective heat exchange surfaces and the manifold configuration yields a low flow resistance across the PMM heat sink, all incorporated in a single layer by the use of AM. Past work has introduced the PMM heat sink concept, but the optimal geometric feature sizes were not explored or identified. The n current study is first to explore design optimization of the PMM heat sink to identify target feature sizes for AM fabrication, assessment of the conditions under which the PMM geometry outperforms other standard microchannel heat sink designs, and inspection of the ability of metal 3D printing process to produce the optimal features. To this end, a reduced-order PMM heat sink model is developed, a gradient-based-multi-objective optimization is performed to identify the optimal feature sizes for different coolants (water and 48/52 water/ethylene glycol mixture) at different flow rates (100 – 500 mL/min), footprint areas (49 – 900 mm2), and channel heights (0.5 – 2.5 mm). The optimization results are benchmarked against an optimized straight microchannel (SMC) heat sink design. Optimized PMM designs offer up to 68% lower thermal resistance at a set pressure drop compared to optimized SMC designs. A pair of SMC and PMM heat sinks optimized for the same operating conditions are 3D printed using direct-metal-laser-sintering (DMLS) of AlSi10Mg. X-ray microtomography is used to characterize the geometry of the 3D-printed parts. The model identifies that optimal membrane gap sizes on the order of ~10s μm are required for the PMM to realize performance advantages compared to SMC heat sinks under the same operating conditions. The performance is predicted to be highly sensitive to this pore size, and even though DMLS is shown to produce parts with gaps as small as 26.7 microns, morphological deviations between the design and as-printed part are shown to lead to noticeable performance differences. Albeit excellent performance potential reinforced by this work, these findings call for further AM process development to ensure reliable, as-predicted PMM heat sinks to realize this potential

Optimization of bipolar plate design for flow and temperature distributions using numerical techniques

Although water is fed controllably into the flow channels in the bipolar plates surrounding the membrane electrode assembly (MEA), the complex flow geometry can lead to non-uniformity of the flow and temperature distribution inside the channels. In addition, non-uniform temperature distribution in the cell will affect the electrochemical process for hydrogen production or fuel cell applications. There are many studies on the theoretical analysis of fuel cells, but not many have been reported on the characteristics of the PEM electrolyzer; In this thesis work, numerical simulations were carried out on the basic bipolar plate given by the Proton Energy Systems in the United States. A 3-D steady state, incompressible flow model was developed. Finite volume method was used to solve the model for flow and temperature distributions inside the channels of the bipolar plate; A parametric study was performed based on number of inlets and outlets and an optimized bipolar plate design was selected. Later, the optimized model was again simulated for two-phase flow. The flow and temperature distributions inside the channels of the new bipolar plate design were found to be uniform even for two-phase flow. Again a parametric study was performed based on volumetric flow rate of water and mass flow rate of oxygen production. Results were tabulated and numerical values were compared with the back of the envelope calculations

Integrated Heat Regenerator (IHR) Designs with Hydrogen Preheater and Thermoelectric Generator for Power Enhancement of a 2 kW Fuel Cell Vehicle

The power train efficiency of fuel cell vehicles (FCV) can be enhanced by improving the hydrogen energy utilization. Based on a mini FCV running on a 2 kW open-cathode Polymer Electrolyte Membrane (PEM) fuel cell, a waste heat recovery system design needs to be developed as an approach towards higher energy efficiency. The novelty of the system is on the integration of thermoelectric generator technology with hydrogen preheating process for a combined heat and power output. This manuscript presents the proposed integrated heat regenerator (IHR) designs, analysed using numerical computational modelling. Three IHR designs were proposed where the main design criteria are (i) a minimum of 10oC hydrogen preheating degree, and (ii) non-parasitic active cooling for the TEG cells. Three design concepts were studied to identify its design and performance limitations. The numerical results were validated with theoretical modelling analysis for hydrogen exit temperatures and TEG surface temperatures. The analysis on predicted fuel cell power enhancement, TEG power generation and waste heat utilization were performed by relating the temperature profiles of the hydrogen reactant and TEG surfaces to fuel cell reaction models and TEG power relationships. A compact IHR design that produced 7.7 to 8 % total power enhancement and suitable in size for a mini FCV was identified for future development work

Generation of stable advective-diffusive chemokine gradients in a three-dimensional hydrogel

Physiologic chemoattractant gradients are shaped by diffusion, advection, binding to an extracellular matrix, and removal by cells. Previous in vitro tools for studying these gradients and the cellular migratory response have required cells to be constrained to a 2D substrate or embedded in a gel devoid of fluid flow. Cell migration in fluid flow has been quantified in the absence of chemoattractant gradients and shown to be responsive to them, but there is a need for tools to investigate the synergistic, or antagonistic, effects of gradients and flow. We present a microfluidic chip in which we generated precisely controlled gradients of the chemokine CCL19 under advective-diffusive conditions. Using torque-actuated membranes situated between a gel region and the chip outlet, the resistance of fluid channels adjacent to the gel region could be modified, creating a controllable pressure difference across the gel at a resolution inferior to 10 Pa. Constant supply and removal of chemokine on either side of the chip facilitated the formation of stable gradients at Péclet numbers between −10 and +10 in a collagen type I hydrogel. The resulting interstitial flow was steady within 0.05 μm s−1 for at least 8 h and varied by less than 0.05 μm s−1 along the gel region. This method advances the physiologic relevance of the study of the formation and maintenance of molecular gradients and cell migration, which will improve the understanding of in vivo observations