Some Smooth and Nonsmooth Traveling Wave Solutions for KP-MEW(2, 2) Equation

In this paper, we consider the KP-MEW(2, 2) equation by the theory of bifurcations of planar dynamical systems when integral constant is considered. The periodic peakon solution and peakon and smooth periodic solutions are given.

Periodic Peakon and Smooth Periodic Solutions for KP-MEW(3,2) Equation

In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for c < 0 , 0 < c < 1 , and c > 1 is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented.

SIMULASI PEREDAMAN GETARAN PADA PEGAS KATUP (VALVE SPRING) SISTEM HIDROLIK DENGAN METODE PID MEMANFAATKAN SIMULINK MATLAB

A simulation of damping vibration on valve spring hydraulic system has been done. This research is a study of the simulation that aims to control excess vibration on valve spring hydraulic system as a result of excitation force that is affected by the changes of pressure periodically, to produce a stable system. The simulation performed by using Matlab simulink with applying a PID method (P, PD, PI and PID) and noticed to variations of proportional constant (Kp), integral constant (Ki) and the derivative constant (Kd). The simulation results obtained show that by combining these three constants Ki, Kp and Kd can dampen the vibration better. For the total excitation force, using the value of Kp = 106, Ki = 7 x 106 and Kd = 6 x 104 can provide damping vibration system response on valve spring with a rise time of 1.2119 s, settling time of 1.2792 s, stable at setpoint 1, error steady state 0% and a small maximum overshoot of 0.3309. This is the result of a stable system response and best compared to the other combinations of the constant values. Keywords : vibration, damper, valve spring, hydraulic system, PID method.

A Closed-Form Solution of Prestressed Annular Membrane Internally-Connected with Rigid Circular Plate and Transversely-Loaded by Central Shaft

In this paper, we analytically dealt with the usually so-called prestressed annular membrane problem, that is, the problem of axisymmetric deformation of the annular membrane with an initial in-plane tensile stress, in which the prestressed annular membrane is peripherally fixed, internally connected with a rigid circular plate, and loaded by a shaft at the center of this rigid circular plate. The prestress effect, that is, the influence of the initial stress in the undeformed membrane on the axisymmetric deformation of the membrane, was taken into account in this study by establishing the boundary condition with initial stress, while in the existing work by establishing the physical equation with initial stress. By creating an integral expression of elementary function, the governing equation of a second-order differential equation was reduced to a first-order differential equation with an undetermined integral constant. According to the three preconditions that the undetermined integral constant is less than, equal to, or greater than zero, the resulting first-order differential equation was further divided into three cases to solve, such that each case can be solved by creating a new integral expression of elementary function. Finally, a characteristic equation for determining the three preconditions was deduced in order to make the three preconditions correspond to the situation in practice. The solution presented here could be called the extended annular membrane solution since it can be regressed into the classic annular membrane solution when the initial stress is equal to zero.

Determination of the internal stress and dislocation velocity stress exponent with indentation stress relaxation test

Indentation stress relaxation tests were carried out on high-purity polycrystalline copper specimens at room temperature with a flat cylindrical indenter. The experimental results showed that the resulting load-time relaxation curves can be described by a power law, which coupled an internal stress and an integral constant between the effective stress and relaxation time. Then the internal stress, integral constant, and dislocation velocity stress exponent can be extracted from load relaxation curves. The derived values from this way were consistent with the results of conventional uniaxial compression stress relaxation tests. These agreements are not only useful to understand deformation (dislocation) mechanisms under the indenter, but also exhibit an attractive potential of measuring nano/micromechanical properties of materials by indentation test.

CORRESPONDENCE BETWEEN DGP BRANE COSMOLOGY AND 5D RICCI-FLAT COSMOLOGY

We discuss the correspondence between the DGP brane cosmology and 5D Ricci-flat cosmology by letting their metrics equal each other. By this correspondence, a specific geometrical property of the arbitrary integral constant I in DGP metric is given and it is related to the curvature of 5D bulk. At the same time, the relation of arbitrary functions μ and ν in a class of Ricci-flat solutions is obtained from DGP brane metric.

INTERACTION OF TWO SIMILAR PLANE DOUBLE LAYERS FOR CaCl2-TYPE ASYMMETRIC ELECTROLYTES AT POSITIVE SURFACE POTENTIAL

The interaction energies between two similar plane double layers for CaCl 2-type asymmetric electrolytes at positive surface potential are expanded in the power series at lower potential and smaller absolute value of integral constant as well as higher potential and larger absolute value of integral constant, respectively. When dimensionless surface potential y0 ≤ 20, the number of the series terms required to obtain the interaction energies with six significant digits are not more than eight if higher potential expressions are combined with lower potential expressions. The accurate numerical results are given and they can be used to check up the validity of approximate expressions that will be obtained. The present results are also fit for Na 2 SO 4-type asymmetric electrolytes at negative surface potential.

Analytic integrals and Poincaré's centre problem

SummaryAs for Poincaré's centre-problem Poincaré [3] himself assumed that if the origin is a centre then there is an integral (constant of motion) being analytic in a neighborhood of the origin. We are going to prove this assumption and vice versa in a concise way by using techniques developed by C. L. Siegel [6].