Uncertainty quantification for stochastic dynamical systems using time-dependent stochastic bases

A novel method based on time-dependent stochastic orthogonal bases for stochastic response surface approximation is proposed to overcome the problem of significant errors in the utilization of the generalized polynomial chaos(GPC) method that approximates the stochastic response by orthogonal polynomials. The accuracy and effectiveness of the method are illustrated by different numerical examples including both linear and nonlinear problems. The results indicate that the proposed method modifies the stochastic bases adaptively, and has a better approximation for the probability density function in contrast to the GPC method.

Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer(DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.

Method of multi-level recursive and application to nonlinear dynamic deformation forecasting

The time-dependence bilinear mixed-regression deformation model and time-dependence bilinear dynamic system deformation model are established for deformation observation series. According to the multi- level recursive method, the time-dependence parameters are first traced and predicted, and then the dynamic system states. Due to the method considering time-dependence of deformation and having stronger adaptability to time-dependence system, it can improve forecast’s precision. It is very effective for data processing of nonlinear dynamic deformation monitoring to make multi-step forecasting.

Enjoy the most beautiful scene now:a memetic algorithm to solve two-fold time-dependent arc orienteering problem

Traditional route planners commonly focus on finding the shortest path between two points in terms of travel distance or time over road networks.However,in real cases,especially in the era of smart cities where many kinds of transportation-related data become easily available,recent years have witnessed an increasing demand of route planners that need to optimize for multiple criteria,e.g.,finding the route with the highest accumulated scenic score along(utility)while not exceeding the given travel time budget(cost).Such problem can be viewed as a variant of arc orienteering problem(AOP),which is well-known as an NP-hard problem.In this paper,targeting a more realistic AOP,we allow both scenic score(utility)and travel time(cost)values on each arc of the road network are time-dependent(2TD-AOP),and propose a memetic algorithm to solve it.To be more specific,within the given travel time budget,in the phase of initiation,for each population,we iteratively add suitable arcs with high scenic score and build a path from the origin to the destination via a complicate procedure consisting of search region narrowing,chromosome encoding and decoding.In the phase of the local search,each path is improved via chromosome selection,local-improvement-based mutation and crossover operations.Finally,we evaluate the proposed memetic algorithm in both synthetic and real-life datasets extensively,and the experimental results demonstrate that it outperforms the baselines.

A Time-Space Adaptive Method for the Schrodinger Equation

In this paper,we present a discretization of the time-dependent Schrodinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space.A truncated Galerkin orthogonality is used to obtain dualitybased a posteriori error estimates that address the temporal and the spatial error separately.Based on this theory,a space-time adaptive solver for the Schrodinger equation is devised.An efficient matrix-free implementation of the differential operator,suited for spectral elements,is used to enable computations for realistic configurations.We demonstrate the performance of the algorithm for the example of matter-field interaction.

Simulation of Vortex Convection in a Compressible Viscous Flow with Dynamic Mesh Adaptation

In this work,vortex convection is simulated using a dynamic mesh adaptation procedure.In each adaptation period,the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the phenomena deviate since the last adaptation.A simple indicator of mesh adaptation that accounts for the solution progression is defined.The generation of dynamic adaptive meshes is based on multilevel refinement/coarsening.The efficiency and accuracy of the present procedure are validated by simulating vortex convection in a uniform flow.Two unsteady compressible turbulent flows involving blade-vortex interactions are investigated to demonstrate further the applicability of the procedure.Computed results agree well with the published experimental data or numerical results.

Computational Study of Scission Neutrons in Low-Energy Fission:Stationary and Time-Dependent Approaches

The emission of scission neutrons from fissioning nuclei is of high practical interest.To study this process we have used the sudden approximation and also a more realistic approach that takes into account the scission dynamics.Numerically,this implies the solution of the bi-dimensional Schr¨odinger equation,both stationary and time-dependent.To describe axially symmetric extremely deformed nuclear shapes,we have used the Cassini parametrization.The Hamiltonian is discretized by using finite difference approximations of the derivatives.The main computational challenges are the solution of algebraic eigenvalue problems and of linear systems with large sparse matrices.We have employed appropriate procedures(Arnoldi and bi-conjugate gradients).The numerical solutions have been used to evaluate physical quantities,like the number of emitted neutrons per scission event,the primary fragments’excitation energy and the distribution of the emission points.

Theoretical investigation on the impact of an oscillating time-dependent pressure gradient on Dean flow in a porous annulus

In this article,a theoretical analysis on flow in a curvilinear horizontal coaxial cylinder with permeable walls has been proposed.Specifically,the transient impact of an oscillating pressure gradient has been taken into account.The non-linear time-dependent partial differential equation accountable for the flow has been transformed using the classical Laplace transform technique.Exact solution of the momentum equation has been obtained in Laplace domain.Due to the intricacy of the Laplace domain solutions,a numerical inversing technique which is established upon the Riemann-sum approximation(RSA)has been utilized to transform the Laplace domain solutions to time domain.Findings reveal that the outcome of suction on the porous walls and boosting the frequency of oscillation renders skin frictions on both walls of the cylinder less effective.The instability of the Dean vortices in the annular gap can be suppressed by amplifying the frequency of oscillating pressure gradient while time is maintained.