Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

ON SHALLOW‐HOLE TEMPERATURE MEASUREMENTS—A TEST STUDY IN THE SALTON SEA GEOTHERMAL FIELD

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 572-583 ◽  
Author(s):  
Tien‐Chang Lee
Keyword(s):  
Numerical Methods ◽  
Ground Surface ◽  
Nonlinear Least Squares ◽  
Geothermal Gradient ◽  
Geothermal Field ◽  
The Other ◽  
Temperature Measurements ◽  
Salton Sea ◽  
Depth Interval ◽  
Average Value

Shallow‐hole (<13 m) temperature measurements made at various depths and/or times may yield reliable values of geothermal gradient and thermal diffusivity if the groundwater table is shallow (a few meters) such that the effect of time‐dependent moisture content and physical properties is negligible. Two numerical methods based on nonlinear least‐squares curve fitting are derived to remove the effect of annual temperature wave at the ground surface. One method can provide information on the gradient and diffusivity as a function of depth while the other gives average value over the depth interval measured. Experiments were carried in six test holes cased with 2 cm OD PVC pipes in the Salton Sea geothermal field. A set of 5 to 7 thermistors was permanently buried inside the individual pipes with dry sand. Consistent gradient determinations have been obtained with both numerical methods from six monthly observations. By linearly extrapolating the depths to the 100°C and 200°C isotherms from the calculated gradients and mean ground temperatures, we have found good agreement with the nearby deep‐well data for four holes. Discrepancy is found for two holes, one of which is located near the field of [Formula: see text] mud volcanoes and the other near the volcanic Red Hill, reflecting complicated local hydrologic conditions.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Concise Equations for Rotor Dynamics Analysis

1995 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
The Other ◽  
Dynamics Analysis ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Abstract Concise equations for rotor dynamics analysis are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two proposed ordering algorithms lead to more compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. This numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency.

scholarly journals A PRACTICAL PERFORMANCE INDEX FOR COMPARING OF OPTIMIZATION SOFTWARE

2014 ◽  
pp. 7-12
Author(s):  
Andrea Attanasio ◽  
Patrizia Beraldi ◽  
Francesca Guerriero
Keyword(s):  
Numerical Methods ◽  
Performance Index ◽  
Relative Efficiency ◽  
Numerical Results ◽  
Optimization Software ◽  
Practical Performance

In this paper we propose a new practical performance index for ranking of numerical methods. This index may be very helpful especially when several methods are tested on a large number of instances, since it provides a concise and precise idea of the relative efficiency of a method with the respect to the others. In order to evaluate the efficiency of the proposed rule, we have applied it to the numerical results presented on previously published papers.

Numerical Simulation on the Electrophoretic Motion of Multiple Particles in Microchannels

2004 ◽  
Author(s):  
Chunzhen Ye ◽  
Dongqing Li
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Electric Field ◽  
Particle Motion ◽  
Outer Region ◽  
Numerical Results ◽  
The Other ◽  
Double Layers ◽  
Rectangular Microchannel ◽  
Moving Particle

This paper considers the electrophoretic motion of multiple spheres in an aqueous electrolyte solution in a straight rectangular microchannel, where the size of the channel is close to that of the particles. This is a complicated 3-D transient process where the electric field, the flow field and the particle motion are coupled together. The objective is to numerically investigate how one particle influences the electric field and the flow field surrounding the other particle and the particle moving velocity. It is also aimed to investigate and demonstrate that the effects of particle size and electrokinetic properties on particle moving velocity. Under the assumption of thin electrical double layers, the electroosmotic flow velocity is used to describe the flow in the inner region. The model governing the electric field and the flow field in the outer region and the particle motion is developed. A direct numerical simulation method using the finite element method is adopted to solve the model. The numerical results show that the presence of one particle influences the electric field and the flow field adjacent to the other particle and the particle motion, and that this influences weaken when the separation distance becomes bigger. The particle motion is dependent on its size, with the smaller particle moving a little faster. In addition, the zeta potential of particle has an effective influence on the particle motion. For a faster particle moving from behind a slower one, numerical results show that the faster moving particle will climb and then pass the slower moving particle then two particles’ centers are not located on a line parallel to the electric field.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Nurnadiah Zamri ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Numerical Results ◽  
Parametric Form ◽  
Solution Point ◽  
New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coefficients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient. 

scholarly journals Limiting stress states in granular avalanches

1998 ◽  
Vol 26 ◽  
pp. 272-276 ◽  
Author(s):  
Y.C. Tai ◽  
J.M.N.T. Gray
Keyword(s):  
Stress State ◽  
Numerical Methods ◽  
Granular Material ◽  
Laboratory Experiments ◽  
Complex Geometry ◽  
The Other ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
Rapid Convergence ◽  
Stress States

The Savage-Hutter theory for granular avalanches assumes that the granular material is in either of two limiting stress states, depending on whether the motion is convergent or divergent. At transitions between convergent and divergent regions, a jump in stress occurs, which necessarily implies that there is a jump in the avalanche velocity and/or its thickness. In this paper, a regularizaron scheme is used, which smoothly switches from one stress state to the other, and avoids the generation of such singular surfaces. The resulting algorithm is more stable than previous numerical methods but shocks can still occur during rapid convergence in the run-out zone. Results are presented from two-dimensional calculations on complex geometry which illustrate that some necking features observed in laboratory experiments can be explained by the regularized Savage-Hutter model.

BIFURCATION STRUCTURE OF SCALAR DIFFERENTIAL DELAYED EQUATIONS

1991 ◽  
Vol 01 (03) ◽  
pp. 657-665 ◽  
Author(s):  
C. P. MALTA ◽  
C. GROTTA RAGAZZO
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Negative Feedback ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Feedback Condition ◽  
Numerical Results ◽  
The Other ◽  
Bifurcation Structure ◽  
Dominant Frequencies

We study periodic solutions of the equation [Formula: see text], with f(X) given by f1(X) = AX(1 − X) or f2(X) = πµ (1 − sin X), grouped in some sets characterized by different dominant frequencies. Numerical results with f(X) = f1(X) are given. One of these sets is shown to exhibit period-doubling cascade in the direction of both parameters A and τ. The other sets are shown to exhibit many other period-doubling cascades as τ is varied establishing a relation between the bifurcation structure within the sets. Furthermore we obtain a lower bound on A and µ for the existence of more complex dynamics. We conjecture that this fact is related to the violation of the so-called "negative-feedback condition."

NUCLEAR COLLISIONS MODELS WITH BOLTZMANN OPERATORS

2000 ◽  
Vol 10 (04) ◽  
pp. 479-505 ◽  
Author(s):  
S. DELLACHERIE ◽  
R. SENTIS
Keyword(s):  
Numerical Methods ◽  
Asymptotic Analysis ◽  
Numerical Results ◽  
Nuclear Collisions

We describe a model related to nuclear collisions using Boltzmann operators. An asymptotic analysis is performed concerning the gain operator for the outgoing particles. Some numerical methods related to this model are also described and numerical results are given.

NUMERICAL SIMULATION ON THE EXISTENCE OF FLUCTUATION OF INSTANTANEOUS AVAILABILITY

2016 ◽  
Vol 40 (5) ◽  
pp. 703-713 ◽  
Author(s):  
Yang Yi ◽  
Ren Si Chao ◽  
Fan Guimei ◽  
Kang Rui
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Failure Rate ◽  
The Other ◽  
Repairable System ◽  
Repair Rate ◽  
Trapezoidal Formula ◽  
Other Hand ◽  
Increasing Functions

This paper considers the fluctuation of the instantaneous availability by numerical methods for a one-unit repairable system. The choices of the failure rate and repair rate are linear or cubic increasing functions. For the equation of instantaneous availability composing of two convolutions, the following numerical methods are used: the composite Simpson formula and the trapezoidal formula. That is to say, the simulated curves of instantaneous availability under any condition are obtained. Through the simulated results, when the failure rate and repair rate are selected as increasing functions, the extremum of simulated curve exists so fluctuation exists. On the other hand, if parameters of increasing functions become smaller, the fluctuation weakens.

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