Kinematic constraint equations

This chapter presents a general methodology for the formulation of the kinematic constraint equations at position, velocity and acceleration levels. Also a brief characterization of the different type of constraints is offered, namely the holonomic and nonholonomic constraints. The kinematic constraints described here are formulated using generalized coordinates. The chapter ends with a general approach to deal with the kinematic analysis of multibody systems.

Equations of motion for constrained systems

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Methods to solve the equations of motion

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Mortar-Techniken zur Behandlung von Grenzschichtproblemen

Elliptic differential equations, finite element method, mortar element method, streamline diffusion FEM, upwind method, numerical method, error estimate, interpolation operator, grid generation, adaptive refinement

Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Numerical approximations of population balance equations in particulate systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2006

Sex-Specific Equations to Estimate Maximum Oxygen Uptake in Cycle Ergometry

AbstractBackground:Aerobic fitness, assessed by measuring VO2max in maximum cardiopulmonary exercise testing (CPX) or by estimating VO2max through the use of equations in exercise testing, is a predictor of mortality. However, the error resulting from this estimate in a given individual can be high, affecting clinical decisions.Objective:To determine the error of estimate of VO2max in cycle ergometry in a population attending clinical exercise testing laboratories, and to propose sex-specific equations to minimize that error.Methods:This study assessed 1715 adults (18 to 91 years, 68% men) undertaking maximum CPX in a lower limbs cycle ergometer (LLCE) with ramp protocol. The percentage error (E%) between measured VO2max and that estimated from the modified ACSM equation (Lang et al. MSSE, 1992) was calculated. Then, estimation equations were developed: 1) for all the population tested (C-GENERAL); and 2) separately by sex (C-MEN and C-WOMEN).Results:Measured VO2max was higher in men than in WOMEN: -29.4 ± 10.5 and 24.2 ± 9.2 mL.(kg.min)-1 (p < 0.01). The equations for estimating VO2max [in mL.(kg.min)-1] were: C-GENERAL = [final workload (W)/body weight (kg)] x 10.483 + 7; C-MEN = [final workload (W)/body weight (kg)] x 10.791 + 7; and C-WOMEN = [final workload (W)/body weight (kg)] x 9.820 + 7. The E% for MEN was: -3.4 ± 13.4% (modified ACSM); 1.2 ± 13.2% (C-GENERAL); and -0.9 ± 13.4% (C-MEN) (p < 0.01). For WOMEN: -14.7 ± 17.4% (modified ACSM); -6.3 ± 16.5% (C-GENERAL); and -1.7 ± 16.2% (C-WOMEN) (p < 0.01).Conclusion:The error of estimate of VO2max by use of sex-specific equations was reduced, but not eliminated, in exercise tests on LLCE.

Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Mathematical and numerical analysis for coagulation-fragmentation equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Numerical analysis of finite volume schemes for population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

singular coagulation and coagulation-fragmentation equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Analytical and numerical investigation of the ultra-relativistic Euler equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.