Macroscopic modeling and simulations of room evacuation

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne–Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-finite element method to solve the problems and present error analysis for the eikonal solver, gradient computation and the second order model yielding a first order convergence. We show that Hughes’ model is incapable of reproducing complex crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally, using the second order model, we study numerically the evacuation of pedestrians from a room through a narrow exit.     

Dynamics modeling and experiments of wave driven robot

Wave driven robots (WDRs) take ocean energies as the power sources and are often used for long-term monitoring of the marine environment. The unique multi-body joint structure and special operation mechanism of a WDR make the dynamics modeling problem unusual. The dynamic model of a WDR was put forward by taking the interconnection of forces and motions between the float body (float) and the submerged glider (glider) into account. Numerical simulation of longitudinal motion and the comparison between simulation and tank test of reciprocating steering motion of the "Ocean Rambler" WDR were carried out. The dynamic model proposed in this paper was consistent with the motion characteristics of "Ocean Rambler" WDR. Simulations of PID heading control demonstrated the unique control characteristics of the WDR, which proved the significance of the established dynamic model of the WDR in control algorithm design.     

Numerical simulations and modeling for stochastic biological systems with jumps

This paper gives a numerical method to simulate sample paths for stochastic differential equations (SDEs) driven by Poisson random measures. It provides us a new approach to simulate systems with jumps from a different angle. The driving Poisson random measures are assumed to be generated by stationary Poisson point processes instead of Lévy processes. Methods provided in this paper can be used to simulate SDEs with Lévy noise approximately. The simulation is divided into two parts: the part of jumping integration is based on definition without approximation while the continuous part is based on some classical approaches. Biological explanations for stochastic integrations with jumps are motivated by several numerical simulations. How to model biological systems with jumps is showed in this paper. Moreover, method of choosing integrands and stationary Poisson point processes in jumping integrations for biological models are obtained. In addition, results are illustrated through some examples and numerical simulations. For some examples, earthquake is chose as a jumping source which causes jumps on the size of biological population.     

Mixing modeling for stochastic simulations of turbulent premixed flames

The use of probability density function (PDF) methods for turbulent combustion simulations is very attractive because arbitrary finite-rate chemistry can be exactly taken into account. However, many real flames involve a variety of mixing regimes (non-premixed, partially-premixed and premixed turbulent combustion), and the development of PDF methods for partiallypremixed and premixed turbulent combustion turned out to be a very challenging task. A promising way to extend the range of applicability of PDF methods to the fast flamelet chemistry of turbulent premixed flames is described here. Simulation results of three turbulent premixed flames demonstrate the suitability of this approach. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of stability and convergence in FD simulations of the 1-D ultrasonic wave propagation

Finite difference (FD) methods are a well established tool for studying the propagation of pulses and waves in nonelementary media. In the present paper, we analyze some different FD schemes for smoothing the interface between two different media, and study their stability and convergence.We find that an improper choice of interface model may lead to unstable or pseudoconvergent recurrence relationships and cause severe errors in the amplitudes of both the reflected and transmitted pulses.     

Finite thermo-viscoplasticity of amorphous glassy polymers: Experiments,modeling and simulations

The contribution is concerned with experimental procedures, constitutive modeling and the numerical simulations of finite thermo-viscoplastic behavior of glassy polymers. The experimental study involves both homogeneous and inhomogeneous tests at different temperatures under isothermal conditions. The true stress-true strain curves obtained from compressive homogeneous uniaxial and plane strain experiments are employed in the identification of adjustable material parameters. In contrast to the existing kinematic approaches to finite plasticity of glassy polymers, we propose a distinct kinematic framework constructed in the logarithmic strain space. This leads us to an algorithmically very attractive, additive kinematic structure in R⁶ similar to the geometrically linear theory. The proposed three-dimensional model is implemented into a finite element code. The load-displacement curves acquired from inhomogeneous experiments are compared against the results obtained from finite element analyses where the material parameters identified from homogeneous experiments are used. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Potential flow simulations of Peregrine-type deep water surface gravity wave packets

Applying a higher order spectral method for potential flow we numerically determine the time evolution of non-linear deep water wave packets originating from initial conditions derived from the Peregrine breather solution of the non-linear Schrödinger equation (NLS). The spatio-temporal evolution of the wave packets qualitatively agrees well with what would be expected from lowest order weakly nonlinear estimates (NLS). Some quantitative discrepancies do, however, exist: The maximum wave envelope amplification appears retarded with respect to the NLS predictions. The amplification factor slightly exceeds the factor known from the NLS solution. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of electromagnetic wave propagation in nonlinear electrodynamics

The eikonal method for an electromagnetic wave propagating according to the laws of non-linear electrodynamics in vacuum in external electromagnetic and gravitational fields is developed. A mathematical model of the propagation of electromagnetic signals in the parameterized post-Maxwellian electrodynamics in vacuum is constructed. As an example of using the proposed method, the angles of the nonlinear electrodynamical and gravitational curvature of the normal wave rays propagating in the field of a charged collapsar are calculated.     

Numerical modeling of dynamic wave effects in rock masses

Spatial dynamic wave effects occurring in rocks with ravines and caverns were studied. The influence exerted by the explosion type and the cavern-to-ravine distance on the formation of spatial dynamic wave patterns and seismograms was analyzed in the case of horizontal and vertical reception lines. The gridcharacteristic method and the full wave joint numerical modeling of elastic and acoustic waves were used.

     

Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions

Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions are investigated. Conservation flows of the dynamic motion are obtained utilizing multiplier approach. Using the unified method, a collection of exact solitary and soliton solutions of Kudryashov-Sinelshchikov equation is presented. Collocation finite element method based on quintic B-spline functions is implemented to the equation to evidence the accuracy of the proposed method by test problems. Stability analysis of the numerical scheme is studied by employing von Neumann theory. The obtained analytical and numerical results are in good agreement.     

Compression moulding simulations of SMC using a multiobjective surrogate-based inverse modeling approach

A multiobjective surrogate-based inverse modeling technique to predict the spatial and temporal pressure distribution numerically during the fabrication of sheet moulding compounds (SMCs) is introduced. Specifically, an isotropic temperature-dependent Newtonian viscosity model of a SMC charge is fitted to experimental measurements via numerical simulations in order to mimic the temporal pressure distribution at two spatial locations simultaneously. The simulations are performed by using the commercial computational fluid dynamics (CFD) code ANSYS CFX-10.0, and the multiobjective surrogate-based fitting procedure proposed is carried out with a hybrid formulation of the NSGA-IIa evolutionary algorithm and the response surface methodology in Matlab. The outcome of the analysis shows the ability of the optimization framework to efficiently reduce the total computational load of the problem. Furthermore, the viscosity model assumed seems to be able to re solve the temporal pressure distribution and the advancing flow front accurately, which can not be said of the spatial pressure distribution. Hence, it is recommended to improve the CFD model proposed in order to better capture the true behaviour of the mould flow.     

Dynamic modeling of electron-ray devices by the method of large particles

We propose a dynamic model of the electron projector of an electron-ray tube, developed using the method of large particles and using statistical methods for modeling the cathode. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 80–85.     

Dynamic modeling of mean-reverting spreads for statistical arbitrage

Statistical arbitrage strategies, such as pairs trading and its generalizations rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. We embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean- reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.     

Galerkin-wavelet modeling of wave propagation: Optimal finite-difference stencil design

In this paper, we describe a method for design of optimal finite-difference stencils for wave propagation problems using an intrinsically explicit Galerkin-wavelet formulation. The method enables an efficient choice of stencils optimal for a certain problem. We compare group velocity curves corresponding to stencils obtained by our choice of wavelet basis and traditional finite-difference schemes. Generally there exist choices of stencils with superior characteristics compared to conventional finite-difference stencils of the same size. Beside gain in accuracy, this leads to large computational savings.     

Thermoacoustic tomography for an integro-differential wave equation modeling attenuation

In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time-convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters. Under the assumption of being able to measure data on the whole boundary, we prove uniqueness and stability, and propose a convergent reconstruction method for a class of smooth variable sound speeds. By a suitable modification of the time reversal technique, we obtain a Neumann series reconstruction formula.     

Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction

A dynamic adaptation method is applied to gas dynamics problems with nonlinear heat conduction. The adaptation function is determined by the condition that the energy equation is quasi-stationary and the grid point distribution is quasi-uniform. The dynamic adaptation method with the adaptation function thus determined and a front-tracking technique are used to solve the model problem of a piston moving in a heat-conducting gas. It is shown that the results significantly depend on the thermal conductivity chosen. The numerical results obtained on a 40-node grid are compared with self-similar solutions to this problem.     

Dynamic modeling of a Stewart platform using the generalized momentum approach

Dynamic modeling of parallel manipulators presents an inherent complexity, mainly due to system closed-loop structure and kinematic constraints.In this paper, an approach based on the manipulator generalized momentum is explored and applied to the dynamic modeling of a Stewart platform. The generalized momentum is used to compute the kinetic component of the generalized force acting on each manipulator rigid body. Analytic expressions for the rigid bodies inertia and Coriolis and centripetal terms matrices are obtained, which can be added, as they are expressed in the same frame. Gravitational part of the generalized force is obtained using the manipulator potential energy. The computational load of the dynamic model is evaluated, measured by the number of arithmetic operations involved in the computation of the inertia and Coriolis and centripetal terms matrices. It is shown the model obtained using the proposed approach presents a low computational load. This could be an important advantage if fast simulation or model-based real-time control are envisaged.     

Mathematical modeling of resonant linear vibratory conveyor with electromagnetic excitation: simulations and experimental results

Vibratory conveyors are commonly used in industry for transporting a wide variety of bulk and particulate materials. Various control structures based on state observers can be found in the literature. However, they are mostly based on simplified mathematical models. In order to obtain a more precise state observer, and consequently better performance and (or) control quality, more detailed mathematical model of the resonant vibratory conveyor is required. Mathematical model of a resonant linear vibratory conveyor driven by an electromagnetic excitation force is presented. Derivation of the mathematical model is based on the kinetic and potential energies, dissipative function of the mechanical system, and Lagrangian formulation. A simulation model is implemented on the basis of the derived mathematical equations. The simulation results are presented and compared to the experimental results obtained by a real industrial vibratory conveyor.