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Lie Symmetry Reductions and Exact Solutions to the Rosenau Equation (2014)

Ben Gao and Hongxia Tian

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-12-15

Description: The Lie symmetry analysis is performed on the Rosenau equation which arises in modeling many physical phenomena. The similarity reductions and exact solutions are presented. Then the exact analytic solutions are considered by the power series method.

Print ISSN: 1687-9120

Electronic ISSN: 1687-9139

Topics: Mathematics , Physics

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Fundamental Solutions for Periodic Media (2014)

Sergey V. Kuznetsov

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-12-15

Description: Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate.

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Topics: Mathematics , Physics

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Investigations on Vehicle Rollover Prevention Using LQG Regulator (2014)

Binda Mridula Balakrishnan and Marimuthu Rajaram

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-12-10

Description: This paper presents results of an initial investigation into vehicle roll model and control strategies suitable for preventing vehicle untripped rollovers. For vehicles that are deemed to be susceptible to wheel-liftoff, various control strategies are implemented in simulation. In this study, the authors propose a method for rollover prevention that does not require such accurate contact information. The validity of the stability margin is shown, and it is used to realize rollover prevention in the direction of the roll. The primary assumption in their implementation is that the vehicle in question is equipped with a conventional controller system.

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Topics: Mathematics , Physics

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Symmetry and Group Theory and Its Application to Few-Body Physics (2014)

Xiao-Yan Gu, Fabien Gatti, Shi-Hai Dong, and Jian-Qiang Sun

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-12-19

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A Spectral Relaxation Approach for Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid over a Permeable Stretching/Shrinking Sheet (2014)

S. S. Motsa, P. Sibanda, J. M. Ngnotchouye, and G. T. Marewo

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-04-29

Description: This paper introduces two novel numerical algorithms for the efficient solution of coupled systems of nonlinear boundary value problems. The methods are benchmarked against existing methods by finding dual solutions of the highly nonlinear system of equations that model the flow of a viscoelastic liquid of Oldroyd-B type in a channel of infinite extent. The methods discussed here are the spectral relaxation method and spectral quasi-linearisation method. To verify the accuracy and efficiency of the proposed methods a comparative evaluation of the performance of the methods against established numerical techniques is given.

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On a System of Two High-Order Nonlinear Difference Equations (2014)

Qianhong Zhang and Wenzhuan Zhang

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-05-06

Description: This paper is concerned with dynamics of the solution to the system of two high-order nonlinear difference equations , , , , where , , and . Moreover the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some numerical examples are considered to show the results obtained.

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Lie Group Method of the Diffusion Equations (2014)

Jian-Qiang Sun, Rong-Fang Huang, Xiao-Yan Gu, and Ling Yu

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-04-30

Description: The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. Numerical results showed that Lie group method is more stable than the corresponding explicit Runge-Kutta method.

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Dynamical Processes and Systems of Fractional Order (2014)

Ming Li, Carlo Cattani, Massimo Scalia, S. C. Lim, and Wen-Sheng Chen

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-03-03

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On a Periodic Solution of the 4-Body Problems (2014)

Jian Chen and Bingyu Li

Hindawi

In: Advances in Mathematical Physics

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Publication Date: 2014-02-12

Description: We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.

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From Pseudorandom Walk to Pseudo-Brownian Motion: First Exit Time from a One-Sided or a Two-Sided Interval (2014)

Aimé Lachal

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2014-03-27

Description: Let be a positive integer, a positive constant and be a sequence of independent identically distributed pseudorandom variables. We assume that the ’s take their values in the discrete set and that their common pseudodistribution is characterized by the (positive or negative) real numbers for any . Let us finally introduce the associated pseudorandom walk defined on by and for . In this paper, we exhibit some properties of . In particular, we explicitly determine the pseudodistribution of the first overshooting time of a given threshold for as well as that of the first exit time from a bounded interval. Next, with an appropriate normalization, we pass from the pseudorandom walk to the pseudo-Brownian motion driven by the high-order heat-type equation . We retrieve the corresponding pseudodistribution of the first overshooting time of a threshold for the pseudo-Brownian motion (Lachal, 2007). In the same way, we get the pseudodistribution of the first exit time from a bounded interval for the pseudo-Brownian motion which is a new result for this pseudoprocess.

Print ISSN: 2090-3332

Electronic ISSN: 2090-3340

Topics: Mathematics

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