Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have been working on the design and implementation of HydLa, a constraint-based modeling language for hybrid systems, with a view to the proper handling of uncertainties and the integration of simulation and verification. HydLa’s constraint hierarchies facilitate...

The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz u...

A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exactWigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in t...

Through considering a large scale single-input, single-output dynamical linear system, we are led to the task of finding a suitable reduced-order model corresponding to that system. Equivalently, we need to successfully approximate the system’s so-called transfer function. To approximate the transfer function the PVL method considers the Lanczos process and its close knit connection to Padé app...

The dynamics of a circular treadmilling low Reynolds number swimmer near a right-angled corner is studied in the asymptotic limit in which the radius of the treadmiller is small. The governing dynamical equations are found explicitly, correct to third order in the swimmer radius, by means of Mellin transform techniques. The existence of arc-like periodic orbits, or ‘hydrodynamic bound states’, ...

Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being use...

This paper treats the quasilinear evolution equations governing the planar motions of incompressible rods. Since incompressibility is here a 2dimensional phenomenon, a thickness variable enters the governing equations in an essential and novel way. These equations have a mathematical structure strikingly different from that for compressible rods. In contrast to the case for compressible rods, t...

Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis, employed mostly in the context of vibro-acoustics, and ray tracing, a popular tool in architectural acoustics. Dynamical energy analysis makes it possible to interp...