Critical behavior for random initial conditions in the one-dimensional fixed-energy Manna sandpile model

2016 ◽  
Vol 94 (1) ◽  
Author(s):  
Sungchul Kwon ◽  
Jin Min Kim
Keyword(s):  
Critical Behavior ◽  
Initial Conditions ◽  
One Dimensional ◽  
Sandpile Model ◽  
Fixed Energy ◽  
Random Initial Conditions ◽  
The One

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

NOTES ON THE DISTRIBUTION OF PHASE SHIFTS

2008 ◽  
Vol 22 (23) ◽  
pp. 2163-2175 ◽  
Author(s):  
MIKLÓS HORVÁTH
Keyword(s):  
Inverse Scattering ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Variational Formula ◽  
Phase Shifts ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Fixed Energy ◽  
Symmetrical Potential ◽  
The One

We consider three-dimensional inverse scattering with fixed energy for which the spherically symmetrical potential is nonvanishing only in a ball. We give exact upper and lower bounds for the phase shifts. We provide a variational formula for the Weyl–Titchmarsh m-function of the one-dimensional Schrödinger operator defined on the half-line.

High Pressure Diesel Engine Modeling

2003 ◽  
Author(s):  
Riccardo Baudille ◽  
Gino Bella ◽  
Rossella Rotondi
Keyword(s):  
Liquid Fuel ◽  
Initial Conditions ◽  
Injection Velocity ◽  
Dimensional Model ◽  
Flow Conditions ◽  
One Dimensional ◽  
Engine Modeling ◽  
Fuel Jet ◽  
Initial Drop ◽  
The One

In multi hole Diesel injectors, cavitation can offer advantages in the development on the fuel spray, because the primary atomization of the liquid fuel jet can be improved due to the enhanced turbulence. Several multi dimensional models of cavitating nozzle flow have been developed in order to provide information about the flow at the exit of a cavitating orifice. In this paper an analytical one-dimensional model, by Sarre et al. [1], to predict the flow conditions at the exit of a cavitating nozzle, is analyzed. The results obtained are compared with the ones obtained using the multi dimensional code Fluent in order to investigate the predictive capability of the one-dimensional code. The model provides initial conditions for multidimensional spray modeling: the effective injection velocity and the initial drop or injected liquid ‘blob’ size. The simulations were performed using an improved version of the KIVA3V code, in which an hybrid break up model, developed by the authors, is used and the results in terms of penetrations and global SMD are compared with the experimental ones. The one dimensional model predicts reasonable discharge coefficient for sharp injector geometry. Where the r/d ratio increases and the cavitation effects appear not clearly marked there are same discrepancies between the one dimensional and the multidimensional approach.

scholarly journals General solutions of the nonlinear PDEs governing the erosion kinetics

2002 ◽  
Vol 8 (1) ◽  
pp. 69-85
Author(s):  
D. E. Panayotounakos ◽  
K. P. Zafeiropoulos
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pde ◽  
Nonlinear Pdes ◽  
General Solutions ◽  
One Dimensional ◽  
Full Complement ◽  
The One

We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.

Analyzing Devaney Chaos of a Sine–Cosine Compound Function System

2018 ◽  
Vol 28 (14) ◽  
pp. 1850176 ◽  
Author(s):  
Hegui Zhu ◽  
Wentao Qi ◽  
Jiangxia Ge ◽  
Yuelin Liu
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Function System ◽  
Topological Transitivity ◽  
One Dimensional ◽  
Devaney’S Chaos ◽  
Chebyshev Map ◽  
Sensitive Dependence ◽  
Sine Map ◽  
The One

The one-dimensional Sine map and Chebyshev map are classical chaotic maps, which have clear chaotic characteristics. In this paper, we establish a chaotic framework based on a Sine–Cosine compound function system by analyzing the existing one-dimensional Sine map and Chebyshev map. The sensitive dependence on initial conditions, topological transitivity and periodic-point density of this chaotic framework is proved, showing that the chaotic framework satisfies Devaney’s chaos definition. In order to illustrate the chaotic behavior of the chaotic framework, we propose three examples, called Cosine–Polynomial (C–P) map, Sine–Tangent (S–T) map and Sine–Exponent (S–E) map, respectively. Then, we evaluate the chaotic behavior with Sine map and Chebyshev map by analyzing bifurcation diagrams, Lyapunov exponents, correlation dimensions, Kolmogorov entropy and [Formula: see text] complexity. Experimental results show that the chaotic framework has better unpredictability and more complex chaotic behaviors than the classical Sine map and Chebyshev map. The results also verify the effectiveness of the theoretical analysis of the proposed chaotic framework.

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