Stochastic resin transfer molding process

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field

Identify Compliance During Software Development Using System Engineering Principles

Errors made during the requirements collection and analysis phase make it very difficult to maintain the software product and cost the company extra costs. The difficulty of directly collecting requirements from stakeholders is due to inconsistencies between the major stakeholder groups, as well as related factors in the collection of requirements itself, as well as the selected methodology for the process of converting stakeholder requirements into development requirements. As a solution, it is necessary to use a high level of prioritization in order to distinguish among many requirements the necessary for successful implementation of the product, as well as to correctly allocate compliance with the requirements in such a way that each group of stakeholders is satisfied, but at the same time setting the goals of the supersystem more priority  than the goals of the subsystem. This article discusses the methodology of system engineering to solve issues related to the identification of possible contradictions of requirements. Keywords: System engineering, requirements engineering, business process, requirements, software product, analysis

On the long-time integration of stochastic gradient systems

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic (stepsize h → 0) convergence behavior of the error of finite time averages. Recently it has been demonstrated, by study of Fokker-Planck operators, that a non-Markovian numerical method [Leimkuhler and Matthews, 2013] generates approximations in the long time limit with higher accuracy order (2nd order) than would be expected from its weak convergence analysis (finite-time averages are 1st order accurate). In this article we describe the transition from the transient to the steady-state regime of this numerical method by estimating the time-dependency of the coefficients in an asymptotic expansion for the weak error, demonstrating that the convergence to 2nd order is exponentially rapid in time. Moreover, we provide numerical tests of the theory, including comparisons of the efficiencies of the Euler-Maruyama method, the popular 2nd order Heun method, and the non-Markovian method

Stochastic resin transfer molding process

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field

Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing faces which can be relevant for operation in non-ideal extreme conditions, notably where external vibrations or disturbances could destabilise the bearing. A modified Reynolds equation is formulated to model the gas flow, retaining the effects of centrifugal inertia which is increasingly important for high-speed operation, and is coupled to the structural equations; spring-mass-damper systems model the axial stator and rotor displacements. A novel model is developed corresponding to a bearing experiencing an external random force to evaluate the resulting induced displacements of the bearing components. The minimum face clearance is obtained from a mapping solver for the modified Reynolds equation and structural equations simultaneously. In the case of random excitations, the solver is combined with a Monte Carlo technique. Evaluation of the average value of the minimum gap and the probability of the gap reaching a prescribed tolerance are provided. Extensive insight is given on the effect of key bearing parameters on the corresponding bearing dynamics

Layer methods for stochastic Navier–Stokes equations using simplest characteristics

We propose and study a layer method for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploiting ideas of the weak sense numerical integration of stochastic differential equations. We prove some convergence results for the proposed method including its first mean-square order. Results of numerical experiments on two model problems are presented

Neural variance reduction for stochastic differential equations

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately optimal control variates and hence reduce variance as trajectories of the SDEs are being simulated. We consider SDEs driven by Brownian motion and, more generally, by L´evy processes including those with infinite activity. For the latter case, we prove optimality conditions for the variance reduction. Several numerical examples from option pricing are presented

Numerical studies of stochastic resonance

A new numerical technique is proposed to study the stochastic resonance (SR) phenomenon. The proposed numerical approach allows to find characteristics of SR faster than the previous ones. The signal-to-noise ratio and phase shifts for a system of noisy coupled oscillators are simulated. The spatiotemporal synchronization is shown by means of trajectory analysis. (orig.)Available from TIB Hannover: RR 5549(322)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman