Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.

A non-orthogonal distributed space-time coded protocol - Part 1:Signal model and design criteria

In this two-part series of papers, a generalized non-orthogonal amplify and forward (GNAF) protocol which generalizes several known cooperative diversity protocols is proposed. Transmission in the GNAF protocol comprises of two phases - the broadcast phase and the cooperation phase. In the broadcast phase, the source broadcasts its information to the relays as well as the destination. In the cooperation phase, the source and the relays together transmit a space-time code in a distributed fashion. The GNAF protocol relaxes the constraints imposed by the protocol of Jing and Hassibi on the code structure. In Part-I of this paper, a code design criteria is obtained and it is shown that the GNAF protocol is delay efficient and coding gain efficient as well. Moreover GNAF protocol enables the use of sphere decoders at the destination with a non-exponential Maximum likelihood (ML) decoding complexity. In Part-II, several low decoding complexity code constructions are studied and a lower bound on the Diversity-Multiplexing Gain tradeoff of the GNAF protocol is obtained.

Target space of an asymmetric chiral gauged wzw model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the chiral gauged SL(2,R) WZW model, with the gauging of subgroups SO(1, 1) in the left and U(1) in the right moving sector, is obtained. We then analyze the symmetries of the background and show the presence of a non-trivial isometry in the canonical parametrization of the WZW model. Using these results, the equivalence of the asymmetric models with the symmetric ones is demonstrated.

AEROSAT - a space-borne sensor for continental aerosols: evaluation of the conceptual model

Even though satellite observations are the most effective means to gather global information in a short span of time, the challenges in this field still remain over continental landmass, despite most of the aerosol sources being land-based. This is a hurdle in global and regional aerosol climate forcing assessment. Retrieval of aerosol properties over land is complicated due to irregular terrain characteristics and the high and largely uncertain surface reflection which acts as `noise' to the much smaller amount of radiation scattered by aerosols, which is the `signal'. In this paper, we describe a satellite sensor the - `Aerosol Satellite (AEROSAT)', which is capable of retrieving aerosols over land with much more accuracy and reduced dependence on models. The sensor, utilizing a set of multi-spectral and multi-angle measurements of polarized components of radiation reflected from the Earth's surface, along with measurements of thermal infrared broadband radiance, results in a large reduction of the `noise' component (compared to the `signal). A conceptual engineering model of AEROSAT has been designed, developed and used to measure the land-surface features in the visible spectral band. Analysing the received signals using a polarization radiative transfer approach, we demonstrate the superiority of this method. It is expected that satellites carrying sensors following the AEROSAT concept would be `self-sufficient', to obtain all the relevant information required for aerosol retrieval from its own measurements.