Reciprocal Transformations in Relativistic Gasdynamics. Lie Group Connections

Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently been shown to have diverse physical applications to nonlinear systems, notably in the analytic treatment of Stefan-type moving boundary problem and in linking inverse scattering systems and integrable hierarchies in soliton theory. Here,invariance under classes of reciprocal transformations in relativistic gasdynamics is shown to be linked to a Lie group procedure.

A simplified simulation procedure for modeling an Active Magnetic Regeneration Cycle in an Electric Vehicle

An alternative to the conventional vapor-compression cycles is the Active Magnetic Refrigeration (AMR) cycle. Some materials, when magnetized or demagnetized, are observed to get heated or cooled. This is known as the Magnetocaloric Effect (MCE). Coupling other components with distinct functionalities in conjunction with the material’s MCE shows promising results when employed for air-conditioning. This is particularly true for air-conditioning applications in an Electric Vehicle (EV), where the electric motor can be used to move the pistons used in the AMR cycle conveniently. Existing physical and mathematical frameworks for modeling the AMR cycle are cumbersome and computationally expensive [10]. The current study proposes a simplified numerical model for analyzing the AMR system's velocity and temperature distributions. The problem has been formulated in a way that averts the need to solve a moving boundary problem, which is one of the chief contributors to the excessive computation time. Several crucial parameters like the operating temperature span have also been calculated to assess the potential of an AMR cycle as an air-conditioning cycle in an EV.

Mathematical Model for Estimating Parameters of Swelling Drug Delivery Devices in a Two-Phase Release

Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient.