Development of an Oxygen Saturation Monitoring System by Embedded Electronics

Measuring Oxygenation of blood (SaO2) plays a vital role in patient’s health monitoring. This is often measured by pulse oximeter, which is standard measure during anesthesia, asthma, operative and post-operative recoveries. Despite all, monitoring Oxygen level is necessary for infants with respiratory problems, old people, and pregnant women and in other critical situations. This paper discusses the process of calculating the level of oxygen in blood and heart-rate detection using a non-invasive photo plethysmography also called as pulsoximeter using the MSP430FG437 microcontroller (MCU). The probe uses infrared lights to measure and should be in physical contact with any peripheral points in our body. The percentage of oxygen in the body is worked by measuring the intensity from each frequency of light after it transmits through the body and then calculating the ratio between these two intensities

Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times $T$, in a class of driven stochastic systems using a theory developed by Engel and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in the path integral form, are characterised by having quadratic actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks flucutation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial function. We then extend our analysis to a stochastically driven system, studied in ( arXiv:1212.0704v2 [cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a moment-generating-function method, for both equilibrium and non - equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary $T$. For dissipated work in the steady state, we compare the large $T$ asymptotic behaviour of our solution to that already obtained in ( arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with the numerical simulations. Our solutions are exact in the low noise limit.Comment: 26 pages, 8 figures. Changes from version 1: Several typos and equations corrected, references added, pictures modified. Version to appear in EPJ

Exact results for the finite time thermodynamic uncertainty relation

We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of the dissipated work at arbitrary times. The uncertainty function (the Fano factor of the dissipated work) is bounded from below by $2k_BT$ as expected, for all times $\tau$, in both steady state and transient regimes. The lower bound is reached at $\tau=0$ as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large $\tau$ for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of $\tau$ as well as other system parameters, implying that the large $\tau$ value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time $\tau_m$, for a range of parameter values. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by $2k_BT$. For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than $2k_BT$.Comment: 11 pages, 11 figures, Version published onlin