A perturbation analysis of spontaneous action potential initiation by stochastic ion channels

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form

How the asymmetry of internal potential influences the shape of I-V characteristic of nanochannels

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics \cite{Apel, Siwy}. The ion current rectification is analyzed. Ion transport through cylindrical nanopores is described by the Smoluchowski equation. The model is considering the symmetric nanopore with asymmetric charge distribution. In this model, the current rectification in asymmetrically charged nanochannels shows a diode-like shape of $I-V$ characteristic. It is shown that this feature may be induced by the coupling between the degree of asymmetry and the depth of internal electric potential well. The role of concentration gradient is discussed

Grown organic matter as a fuel raw material resource

An extensive search was made on biomass production from the standpoint of climatic zones, water, nutrients, costs and energy requirements for many species. No exotic species were uncovered that gave hope for a bonanza of biomass production under culture, location, and management markedly different from those of existing agricultural concepts. A simulation analysis of biomass production was carried out for six species using conventional production methods, including their production costs and energy requirements. These estimates were compared with data on food, fiber, and feed production. The alternative possibility of using residues from food, feed, or lumber was evaluated. It was concluded that great doubt must be cast on the feasibility of producing grown organic matter for fuel, in competition with food, feed, or fiber. The feasibility of collecting residues may be nearer, but the competition for the residues for return to the soil or cellulosic production is formidable

Use of mathematical modeling to study pressure regimes in normal and Fontan blood flow circulations

We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. We present numerical simulations of the cardiac pressure-volume cycle and study the effect of pulmonary resistance on cardiac output. We analyze solutions of two initial-boundary value problems for a non-linear parabolic partial differential equation (PDE models) with switching in the time dynamic boundary conditions which model blood pressure distribution in the cardiovascular system with and without Fontan surgery. We also obtain necessary conditions for parameter values of the PDE models for existence and uniqueness of non-negative bounded periodic solutions.Comment: 32 pages, 6 figures, 1 tabl

On the Accuracy of A.C. Flux Leakage, Eddy Current, EMAT and Ultrasonic Methods of Measuring Surface Connecting Flaws in Seamless Steel Tubing

The objective of this study was to perform a comparative experimental evaluation to determine the detection sensitivity, classification (fJaw type) and depth sizing accuracy of A.C. flux leakage, single-frequency eddy current, electromagnetic acoustic transducer (EMAT) generated surface waves, and broadband ultrasonic methods for the measurement of complex surface connecting flaws in hot rolled, seamless, ferritic tubing. Since it was of interest to invest NDE techniques over a wide range of capabilities, tubing having flaw depths far exceeding industry standards was tested and evaluated. Results of the study will be used to provide a benchmark assessment of these NDE methods, from which decisions concerning production test systems can be made

Generation of finite wave trains in excitable media

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.Comment: 6 pages, 6 figure

A prototype acid spray scrubber for absorbing ammonia emissions from exhaust fans of animal buildings

Mitigation of ammonia (NH3) emissions from animal production buildings has been a challenge because of the large volume of low NH3 concentration laden air being released. Among emission mitigation technologies for concentrated animal feeding operations, acid spray scrubbers have the greatest potential for adaptation to the existing large animal facilities because of their lower fan airflow reduction, ability to simultaneously remove particulate and gaseous pollutants, and viability for zero or less waste generation by recycling effluents as liquid fertilizer. A multi-stage wet scrubber prototype that can be operated with a maximum of three stages was developed and optimized for reducing NH3 emissions using simulated conditions typically encountered at an animal building exhaust. The parameters optimized for a single-stage wet scrubber include nozzle type, nozzle operating pressure, sulfuric acid concentration, spray coverage, and air retention time. The optimized single-stage wet scrubber settings can remove emissions from 60% ±1% at 5 ppmv inlet NH3 concentration (IAC) to 27% ±2% at 100 ppmv IAC at a normal exhaust superficial air velocity (SAV) of 6.6 m s-1. A high concentration of droplets inside the contact chamber increased the rate of inter-collision between droplets, which led to high droplet coagulation and decreased surface area for gas-liquid contact. These phenomena were prevented by operating the nozzles in the higher stages co-current to the airflow and by using fewer nozzles in higher stage. The two-stage and three-stage wet scrubbers were therefore optimized by determining the least number of nozzles in each stage that provided the most effective NH3 removal. The optimized two-stage scrubber could remove NH3 emissions from 60% ±0% at 5 ppmv IAC and 35% ±1% at 100 ppmv IAC. The optimized three-stage scrubber could remove emissions from 63% ±3% at 5 ppmv IAC and 36% ±3% at 100 ppmv IAC. Airflow retention time was found to significantly affect NH3 absorption. Reducing the superficial air velocity to 3.3 m s-1 from 6.6 m s-1, which increased the air retention time from 0.2 s to 0.4 s, improved NH3 removal efficiencies to 98% ±3% at 5 ppmv IAC and 46% ±2% at 100 ppmv IAC for the single-stage scrubber. Similarly, the performance of the two-stage scrubber at a SAV of 3.3 m s-1 improved to 77% ±0% at 20 ppmv IAC and 57% ±1% at 100 ppm IAC. Lastly, the performance of the three-stage scrubber at a SAV of 3.3 m s-1 improved to 70% ±1% at 30 ppmv IAC and 64% ±1% at 100 ppmv IAC. It was observed that the three-stage wet scrubber did not increase the overall wet scrubber performance, as predicted theoretically. Further studies are needed so that the application of these scrubber designs becomes feasible for treating air emissions from animal buildings. The wet scrubber caused an additional backpressure of 27.5 Pa, resulting in about 8% airflow reduction for a fan operating at 12.5 Pa

Use of soil moisture information in yield models

There are no author-identified significant results in this report

Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received, and cells change type up to a given distance, or under other conditions, the differentiation process propagates through the whole domain. When the signal diminishes hysteresis is observed