Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.

Non-Linear Numerical Simulation of Coal and Gas Outburst as a Coupling Instability Problem of Solid-Fluid Biphase Media

Based on the theory of continuum mechanics of multi-pbase media, a mathematical model and non-linear FEM equation of the coupling instability problem of solid-fluid biphase media for coal-methane outburst under finite deformation are established. The critical conditions of the surface instability are presented as the singularity of the total stiffness matrices of the coal body for coal-methaue outburst. That means the deformtion or the coal body emerges bifurcatiou phenomena. The numerical simulation of a typical outburst is made.

Numerical Simulation on Thermal Stress of Large-scale Bearing Roller during Heating Process of Final Heat Treatment

hi this paper, the non-linear finite element method had been applied to calculate the thermal stress evolving process of the large-scale bearing roller during heating process of final heat treatment. It was found that two stress peaks appeared during heating process and the second stress peak was higher than the first. If the preheating time was elongated, the second stress peak was reduced distinctly. Therefore, the pre-heating time should be elongated suitably to ensure safety in the practical manufacture process.

Simulation of Diode-Pumped Q-Switched Nd:YAG Laser Generating Eye-Safe Signal in IOPO Environment

Numerical simulation of diode-pumped Q-switched Nd:YAG laser leading to the generation of eye-safe signal in singly resonant Intracavity Optical Parametric Oscillator (IOPO) is presented. Starting from rate equations, the time dependent laser equations have been solved numerically, whereas the space-dependent OPO equations analytically. Our results show that 1.4 J diode laser (810 nm) pulse with 200 msec width, delivers 30 mJ Nd:YAG laser (1064 nm) pulse with 5 n-second width. This Nd:YAG laser further generates 9 mJ eye safe signal (1570 nm) pulse with 2.5 n-second width.

Non-linear characteristics of Rayleigh-Taylor instable perturbations

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The ampli- tude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.

Non-Linear Mathematical Model of the Interaction between Tumor and Oncolytic Viruses

A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.

Analytical solution of coupled non-linear second order differential equations in enzyme kinetics

The coupled system of non-linear second-order reaction differential equation in basic enzyme reaction is formulated and closed analytical ex-pressions for substrate and product concentra-tions are presented. Approximate analytical me-thod (He’s Homotopy perturbation method) is used to solve the coupled non-linear differential equations containing a non-linear term related to enzymatic reaction. Closed analytical expres-sions for substrate concentration, enzyme sub-strate concentration and product concentration have been derived in terms of dimensionless reaction diffusion parameters k, and us-ing perturbation method. These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain.

Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method

This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.

Analytical Solutions of Some Two-Point Non-Linear Elliptic Boundary Value Problems

Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.

Fault Diagnosis for Non-linear System Based On Adaptive Fuzzy System

Although lots of valuable results for fault diagnosis based on model have been achieved in linear system, it is difficult to apply these results to non-linear system due to the difficulty of modeling the non-linear system by analysis. Adaptive Fuzzy system provides a way for solving this problem because it can approximate any non-linear system at any accuracy. The key for adaptive Fuzzy system to solve problem is its learning ability, so the authors present a learning algorithm for Adaptive fuzzy system, which can build the system's model by learning from the measurement data as well as experience knowledge with high accuracy. Furthermore, the experiment using the learning algorithm to model a servo-mechanism and to construct the fault diagnosis system based on the model is carried out, the results is very good.

NUMERICAL SIMULATION OF NON-LINEAR STERN WAVES

This paper deals with the 2—D numerical simulation of non-linear waves behind the stern of a flat-bottomed ship.The fluid is assumed inviscid and imcompressible.Fully non-linear dynamic and kinematic boundary condi- tions are applied on free surface,and suitable radiation condition is applied at outflow boundary.Time-dependent stream functions are used as the dependent variables to approach the steady state solution.Finite difference meth- ods and body-fitted coordinates are employed to obtain the numerical solution.Physical tests with a schematized flat-bottomed ship model are performed to validate the computational scheme.Results from both computations and experiments seem to be in reasonable agreement.

Quadratic and cubic eddy-viscosity models in turbulent supercavitating flow computation

Quadratic and cubic non-linear eddy-viscosity turbulence models(NLEVM) with low Reynolds number(Re) correction were presented to provide better description of anisotropic turbulence stresses in the numerical prediction of supercavitating flows,which are accompanied with large density ratio and large-scaled swirling flow structures.The applications of the NLEVM were carried out through a self-developed cavitation codes,coupled with a cavitation model based on the transport equation of liquid phase.These NLEVM were verified capable of capturing more accurate macroscopic shape and hydrodynamic property of supercavity by the benchmark problems of supercavities over simple objects.Finally,the cubic NLEVM was further applied to the numerical prediction of supercavitating flow around a complex submerged vehicle.The corresponding cavitation behaviors were explored in detail to provide beneficial experience for further research.

Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process

The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation, based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear. It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.

On the direct searches for non-smooth stochastic optimization problems

Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.

Study of the internal characteristics of the stall in a centrifugal pump with a cubic non-linear SGS model

The stall in a centrifugal pump impeller under a quarter-load condition is investigated by using a third-order SGS model named the DCNM, for a better understanding of the rotation effect on the stall phenomenon. The study of the distributions of the Reynolds stresses, the production tei*m and the rotation term reveals that the production and the rotation jointly result in the non-uniform Reynolds stress distribution. Further study of the two components of the production and the rotation shows that they jointly transport a certain energy from the Reynolds component R、to Ruu.

Autoregressive neural networks with exogenous variables for indoor temperature prediction in buildings

Thermal models of buildings are helpful to forecast their energy use and to enhance the control of their mechanical systems.However,these models are building-specific and require a tedious,error-prone and time-consuming development effort relying on skilled building energy modelers.Compared to white-box and gray-box models,data-driven(black-box)models require less development time and a minimal amount of information about the building characteristics.In this paper,autoregressive neural network models are compared to gray-box and black-box linear models to simulate indoor temperatures.These models are trained,validated and compared to actual experimental data obtained for an existing commercial building in Montreal(QC,Canada)equipped with roof top units for air conditioning.Results show that neural networks mimic more accurately the thermal behavior of the building when limited information is available,compared to gray-box and black-box linear models.The gray-box model does not perform adequately due to its under-parameterized nature,while the linear models cannot capture non-linear phenomena such as radiative heat transfer and occupancy.Therefore,the neural network models outperform the alternative models in the presented application,reaching a coefficient of determination R2 up to 0.824 and a root mean square error down to 1.11℃,including the error propagation over time for a 1-week period with a 5-minute time-step.When considering a 50-hour time horizon,the best neural networks reach a much lower root mean square error of around 0.6℃,which is suitable for applications such as model predictive control.

The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

This paper proposes various stages of the hepatitis B virus(HBV)besides its transmissibility and nonlinear incidence rate to develop an epidemic model.The authors plan the model,and then prove some basic results for the well-posedness in term of boundedness and positivity.Moreover,the authors find the threshold parameter R0,called the basic/effective reproductive number and carry out local sensitive analysis.Furthermore,the authors examine stability and hence condition for stability in terms of R0.By using sensitivity analysis,the authors formulate a control problem in order to eradicate HBV from the population and proved that the control problem actually exists.The complete characterization of the optimum system was achieved by using the 4th-order Runge-Kutta procedure.