Variable Modified Chaplygin Gas and Accelerating Universe

In this letter, I have proposed a model of variable modified Chaplygin gas and shown its role in accelerating phase of the universe. I have shown that the equation of state of this model is valid from the radiation era to quiessence model. The graphical representations of statefinder parameters characterize different phase of evolution of the universe. All results presented in the letter concerns the case $k=0$.Comment: 7 Latex pages, 5 figures, revtex styl

The use of disaggregated demand information to improve forecasts and stock allocation during sales promotions: a simulation and optimisation study using supermarket loyalty card data

Our work highlights the importance of using disaggregated demand information at store level to improve sales forecasts and stock allocation during sales promotions. Monte Carlo simulation and optimisation modelling were used to estimate short-term promotional impacts. Supermarket loyalty card data was used from a major UK retailer to identify the benefits of using disaggregated demand data for improved forecasting and stock allocation. The results suggest that there is a high degree of heterogeneity in demand at individual store level due to number of factors including the weather, the characteristics of shoppers, the characteristics of products and store format, all of which conspire to generate significant variation in promotional uplifts. The paper is the first to use supermarket loyalty card data to generate store level promotional forecasts and quantify the benefits of disaggregating the allocation of promotional stock to the level of individual stores rather than regional distribution centres

Slow-light enhanced light-matter interactions with applications to gas sensing

Optical gas detection in microsystems is limited by the short micron scale optical path length available. Recently, the concept of slow-light enhanced absorption has been proposed as a route to compensate for the short path length in miniaturized absorption cells. We extend the previous perturbation theory to the case of a Bragg stack infiltrated by a spectrally strongly dispersive gas with a narrow and distinct absorption peak. We show that considerable signal enhancement is possible. As an example, we consider a Bragg stack consisting of PMMA infiltrated by O2. Here, the required optical path length for visible to near-infrared detection (~760 nm) can be reduced by at least a factor of 10^2, making a path length of 1 mm feasible. By using this technique, optical gas detection can potentially be made possible in microsystems

A Smart IoT-Based Prototype System for Rehabilitation Monitoring

Smart healthcare is growing significantly in the healthcare sector due to the Internet of Things. A remote monitoring system is one of the smart healthcare implementations for rehabilitating stroke patients. Nowadays, as the COVID-19 pandemic continues to spread, patients undergoing home rehabilitation have difficulty meeting with their physicians due to movement constraints. In addition, the healthcare facilities are devoted to treating patients with COVID-19. As a result, physicians and patients could not frequently meet to gather their rehabilitation progress. This study involves developing a prototype to monitor a post-stroke patient's rehabilitation process using the Arduino Nano 33 Bluetooth Low Energy (BLE) and force-sensing resistor (FSR). The prototype analyzes critical aspects of the rehabilitation process based on handgrip, heart rate, sleep, and step tracking measurements. The results of the handgrip, heart rate, sleep, and step tracking measurements are evaluated for various types of subjects and six testing approaches showed an accurate and consistent results. However, experiments partially success with a small error is detected while tracking the steps of each subject. Several recommendations are highlighted to improve the prototype using other sensors such as force sensing resistor and flex sensor for handgrip force transducer, electromyogram (EMG) sensor for stroke-patients rehabilitation, and others

A Smart IoT-Based Prototype System for Rehabilitation Monitoring

Smart healthcare is growing significantly in the healthcare sector due to the Internet of Things. A remote monitoring system is one of the smart healthcare implementations for rehabilitating stroke patients. Nowadays, as the COVID-19 pandemic continues to spread, patients undergoing home rehabilitation have difficulty meeting with their physicians due to movement constraints. In addition, the healthcare facilities are devoted to treating patients with COVID-19. As a result, physicians and patients could not frequently meet to gather their rehabilitation progress. This study involves developing a prototype to monitor a post-stroke patient's rehabilitation process using the Arduino Nano 33 Bluetooth Low Energy (BLE) and force-sensing resistor (FSR). The prototype analyzes critical aspects of the rehabilitation process based on handgrip, heart rate, sleep, and step tracking measurements. The results of the handgrip, heart rate, sleep, and step tracking measurements are evaluated for various types of subjects and six testing approaches showed an accurate and consistent results. However, experiments partially success with a small error is detected while tracking the steps of each subject. Several recommendations are highlighted to improve the prototype using other sensors such as force sensing resistor and flex sensor for handgrip force transducer, electromyogram (EMG) sensor for stroke-patients rehabilitation, and others

Dynamics of Logamediate and Intermediate Scenarios in the Dark Energy Filled Universe

We have considered a model of two component mixture i.e., mixture of Chaplygin gas and barotropic fluid with tachyonic field. In the case, when they have no interaction then both of them retain their own properties. Let us consider an energy flow between barotropic and tachyonic fluids. In both the cases we find the exact solutions for the tachyonic field and the tachyonic potential and show that the tachyonic potential follows the asymptotic behavior. We have considered an interaction between these two fluids by introducing a coupling term. Finally, we have considered a model of three component mixture i.e., mixture of tachyonic field, Chaplygin gas and barotropic fluid with or without interaction. The coupling functions decays with time indicating a strong energy flow at the initial period and weak stable interaction at later stage. To keep the observational support of recent acceleration we have considered two particular forms (i) Logamediate Scenario and (ii) Intermediate Scenario, of evolution of the Universe. We have examined the natures of the recent developed statefinder parameters and slow-roll parameters in both scenarios with and without interactions in whole evolution of the universe.Comment: 28 pages, 20 figure

Expanding Universe: Thermodynamical Aspects From Different Models

The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: $w(z)=w_{0}+w_{1}\ln(1+z)$ & $w(z)=-1+\frac{(1+z)}{3}\frac{A_{1}+2A_{2}(1+z)}{A_{0}+2A_{1}(1+z)+A_{2}(1+z)^{2}}$. The time scale of instability for this two models is discussed. In the paper we then generalize our result and arrive at general expression for energy density irrespective of the model. The thermodynamical stability for both of the model and the general case is discussed from this viewpoint. We also arrive at a condition on the limiting behavior of thermodynamic parameter to validate the third law of thermodynamics and interpret the general mathematical expression of integration constant $U_{0}$ (what we get while integrating energy conservation equation) physically relating it to number of micro states. The constraint on the allowed values of the parameters of the models is discussed which ascertains stability of universe. The validity of thermodynamical laws within apparent and event horizon is discussed.Comment: 16 pages, 3 figures(Accepted for publication in "Astrophysics and Space Science"

Interaction between Tachyon and Hessence (or Hantom) dark energies

In this paper, we have considered that the universe is filled with tachyon, hessence (or hantom) dark energies. Subsequently we have investigated the interactions between tachyon and hessence (hantom) dark energies and calculated the potentials considering the power law form of the scale factor. It has been revealed that the tachyonic potential always decreases and hessence (or hantom) potential increases with corresponding fields. Furthermore, we have considered a correspondence between the hessence (or hantom) dark energy density and new variable modified Chaplygin gas energy density. From this, we have found the expressions of the arbitrary positive constants B0 and C of new variable modified Chaplygin gas