Multiple solutions of steady-state Poisson-Nernst-Planck equations with steric effects

Experiments measuring currents through single protein channels show unstable currents. Channels switch between 'open' or 'closed' states in a spontaneous stochastic process called gating. Currents are either (nearly) zero or at a definite level, characteristic of each type of protein, independent of time, once the channel is open. The steady state Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) describe steady current through the open channel quite well, in a wide variety of conditions. Here we study the existence of multiple solutions of steady state PNP-steric equations to see if they themselves, without modification or augmentation, can describe two levels of current. We prove that there are two steady state solutions of PNP-steric equations for (a) three types of ion species (two types of cations and one type of anion) with a positive constant permanent charge, and (b) four types of ion species (two types of cations and their counter-ions) with a constant permanent charge but no sign condition. The excess currents (due to steric effects) associated with these two steady state solutions are derived and expressed as two distinct formulas. Our results indicate that PNP-steric equations may become a useful model to study spontaneous gating of ion channels. Spontaneous gating is thought to involve small structural changes in the channel protein that perhaps produce large changes in the profiles of free energy that determine ion flow. Gating is known to be modulated by external structures. Both can be included in future extensions of our present analysis.Comment: 27 pages, 5 figure

Cognitive trait model for persistent and fine-tuned student modelling in adaptive virtual learning environments : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Science in Information Systems at Massey University

The increasing need for individualised instructional in both academic and corporate training environment encourages the emergence and popularity of adaptivity in virtual learning environments (VLEs). Adaptivity can be applied in VLEs as adaptivity content presentation, which generates the learning content adaptively to suit the particular learner's aptitude, and as adaptive navigational control, which dynamically modifies the structure of the virtual learning environment presented to the learner in order to prevent overloading the learner's cognitive load. Techniques for both adaptive content presentation and adaptive navigational control need to be integrated in a conceptual framework so their benefits can be synthesised to obtain a synergic result. Exploration space control (ESC) theory attempts to adjust the learning space, called exploration space, to allow the learners to reach an adequate amount of information that their cognitive load is not overloaded. Multiple presentation (MR) approach provides guidelines for the selection of multimedia objects for both the learning content presentation and as navigational links. ESC is further formalised by including the consideration of individual learner's cognitive traits, which are the cognitive characteristics and abilities the learner relevant in the process of learning. Cognitive traits selected in the formalisation include working memory capacity, inductive reasoning skill, associative learning skill, and information processing speed. The formalisation attempts to formulate a guideline on how the learning content and navigational space should be adjusted in order to support a learner with a particular set of cognitive traits. However, in order to support the provision of adaptivity, the learners and their activities in the VLEs need to be profiled; the profiling process is called student modelling. Student models nowadays can be categorised into state models, and process models. State models record learners' progress as states (e.g. learned, not learned), whereas a process model represents the learners in term of both the knowledge they learned in the domain, and the inference procedures they used for completing a process (task). State models and process models are both competence-based, and they do not provide the information of an individual's cognitive abilities required by the formalisation of exploration space control. A new approach of student modelling is required, and this approach is called cognitive trait model (CTM). The basis of CTM lies in the field of cognitive science. The process for the creation of CTM includes the following subtasks. The cognitive trait under inquiry is studied in order to find its indicative signs (e.g. sign A indicates high working memory capacity). The signs are called the manifests of the cognitive trait. Manifests are always in pairs, i.e. if manifest A indicates high working memory capacity, A's inverse, B, would indicates low working memory capacity. The manifests are then translated into implementation patterns which are observable patterns in the records of learner-system interaction. Implementation patterns are regarded as machine-recognisable manifests. The manifests are used to create nodes in a neural network like structure called individualised temperament network (ITN). Every node in the ITN has its weight that conditions and is conditioned by the overall result of the execution of ITN. The output of the ITN's execution is used to update the CTM. A formative evaluation was carried out for a prototype created in this work. The positive results of the evaluation show the educational potential of the CTM approach. The current CTM only cater for the working memory capacity, in the future research more cognitive traits will be studied and included into the CTM

MEMS flow sensors for nano-fluidic applications

This paper presents micromachined thermal sensors for measuring liquid flow rates in the nanoliter-per-minute range. The sensors use a boron-doped polysilicon thinfilm heater that is embedded in the silicon nitride wall of a microchannel. The boron doping is chosen to increase the heater’s temperature coefficient of resistance within tolerable noise limits, and the microchannel is suspended from the substrate to improve thermal isolation. The sensors have demonstrated a flow rate resolution below 10 nL/min, as well as the capability for detecting micro bubbles in the liquid. Heat transfer simulation has also been performed to explain the sensor operation and yielded good agreement with experimental data

The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids

We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short (20 ps) molecular dynamics trajectory is used to obtain the vibrational density of states (DoS) which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase (highly fluidic), described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3Ng, the total number of gas phase modes [3Ng0 for a solid and 3Ng3(N–1) for temperatures and pressures for which the system is a gas]. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids (and gases and solids)

Surface micromachined electrostatically actuated micro peristaltic pump

An electrostatically actuated micro peristaltic pump is reported. The micro pump is entirely surface micromachined using a multilayer parylene technology. Taking advantage of the multilayer technology, the micro pump design enables the pumped fluid to be isolated from the electric field. Electrostatic actuation of the parylene membrane using both DC and AC voltages was demonstrated and applied to fluid pumping based on a 3-phase peristaltic sequence. A maximum flow rate of 1.7 nL min^–1 and an estimated pumping pressure of 1.6 kPa were achieved at 20 Hz phase frequency. A dynamic analysis was also performed with a lumped-parameter model for the peristaltic pump. The analysis results allow a quantitative understanding of the peristaltic pumping operation, and correctly predict the trends exhibited by the experimental data. The small footprint of the micro pump is well suited for large-scale integration of microfluidics. Moreover, because the same platform technology has also been used to fabricate other devices (e.g. valves, electrospray ionization nozzles, filters and flow sensors), the integration of these different devices can potentially lead to versatile and functional micro total analysis systems (µTAS)