scholarly journals Measuring adaptation with a sinusoidal perturbation function

2012 ◽  
Vol 208 (1) ◽  
pp. 48-58 ◽  
Author(s):  
Todd E. Hudson ◽  
Michael S. Landy
Keyword(s):  
Perturbation Function

Sound Propagation in Dilute Polyatomic Gases

1972 ◽  
Vol 27 (4) ◽  
pp. 583-592
Author(s):  
H. Moraal ◽  
F. Mccourt
Keyword(s):  
Pressure Range ◽  
Sound Propagation ◽  
Plane Waves ◽  
Point Of View ◽  
Perturbation Function ◽  
Sound Waves ◽  
Polyatomic Gas ◽  
Measured Pressure ◽  
Theory And Experiment ◽  
Good Agreement

Abstract Sound propagation in dilute pure gases, both monatomic and polyatomic, has been considered from the point of view of the Waldmann-Snider equation. It is shown that the commonly employed assumption that sound propagation in gases is equivalent to the propagation of plane waves is valid only in the region where collisions restore equilibrium faster than it is perturbed by the sound waves. A systematic truncation procedure for an expansion of the perturbation function in irreducible Cartesian tensors is introduced and then illustrated in solutions for three specific kinds of molecules, helium, nitrogen and rough spheres. The agreement between theory and experiment is rather good for sound absorption in the region where the ratio of the collision and sound frequencies is greater than 1.5. The agreement in the case of dispersion is good over the whole measured pressure range. One useful result obtained is to show the polyatomic gas calculations in second approximation have as good agreement with experiment as the calculations for noble gases in third approximation. This can be related to the possession by the polyatomic gas of a bulk viscosity which dominates in sound propagation.

scholarly journals Realistic f(T) model describing the de Sitter epoch of the dark energy dominated universe

2015 ◽  
Vol 93 (10) ◽  
pp. 1050-1056 ◽  
Author(s):  
S.B. Nassur ◽  
A.V. Kpadonou ◽  
M.E. Rodrigues ◽  
M.J.S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Model Checking ◽  
Exponential Model ◽  
Effective Parameter ◽  
Perturbation Function ◽  
De Sitter ◽  
Torsion Scalar ◽  
Theory Of Gravity

We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the torsion scalar. We focus our attention on a cosmological feature of a f(T) model, checking whether it may describe the de Sitter stage of the current universe according to the evolution of the redshift, z. Our results show that the model reproduces the de Sitter stage only for low redshifts, where the perturbation function approached zero, whereas the effective parameter of the equation of state goes to –1, which is the expected behavior for any model able to reproduce the de Sitter stage.

scholarly journals An application of chaos gray-encoded genetic algorithm for Philip infiltration model

2018 ◽  
Vol 22 (4) ◽  
pp. 1581-1588 ◽  
Author(s):  
Kai-Wen Wang ◽  
Xiao-Hua Yang ◽  
Yu-Qi Li ◽  
Chang-Ming Liu ◽  
Xing-Jian Guo
Keyword(s):  
Genetic Algorithm ◽  
Numerical Calculation ◽  
Optimization Algorithm ◽  
Optimization Technique ◽  
Parameters Estimation ◽  
Physical Parameters ◽  
Perturbation Function ◽  
Infiltration Model ◽  
Cumulative Infiltration ◽  
Relationship Of

To improve the precision of parameters? estimation in Philip infiltration model, chaos gray-coded genetic algorithm was introduced. The optimization algorithm made it possible to change from the discrete form of time perturbation function to a more flexible continuous form. The software RETC and Hydrus-1D were applied to estimate the soil physical parameters and referenced cumulative infiltration for seven different soils in the USDA soil texture triangle. The comparisons among Philip infiltration model with different numerical calculation methods showed that using optimization technique can increase the Nash and Sutcliffe efficiency from 0.82 to 0.97, and decrease the percent bias from 14% to 2%. The results indicated that using the discrete relationship of time perturbation function in Philip infiltration model?s numerical calculation underestimated model?s parameters, but this problem can be corrected a lot by using optimization algorithm. We acknowledge that in this study the fitting of time perturbation function, Chebyshev polynomial with order 20, did not perform perfectly near saturated and residue water content. So exploring a more appropriate function for representing time perturbation function is valuable in the future.

scholarly journals $$\alpha $$-Dirac-harmonic maps from closed surfaces

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Jürgen Jost ◽  
Jingyong Zhu
Keyword(s):  
Harmonic Maps ◽  
Harmonic Map ◽  
Nonpositive Curvature ◽  
Existence Problem ◽  
Perturbation Function ◽  
Regularity Theorem ◽  
Closed Surfaces ◽  
Palais Smale Condition ◽  
Target Manifold

Abstract$$\alpha $$ α -Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $$\alpha $$ α -harmonic maps that were introduced by Sacks–Uhlenbeck to attack the existence problem for harmonic maps from closed surfaces. For $$\alpha >1$$ α > 1 , the latter are known to satisfy a Palais–Smale condition, and so, the technique of Sacks–Uhlenbeck consists in constructing $$\alpha $$ α -harmonic maps for $$\alpha >1$$ α > 1 and then letting $$\alpha \rightarrow 1$$ α → 1 . The extension of this scheme to Dirac-harmonic maps meets with several difficulties, and in this paper, we start attacking those. We first prove the existence of nontrivial perturbed $$\alpha $$ α -Dirac-harmonic maps when the target manifold has nonpositive curvature. The regularity theorem then shows that they are actually smooth if the perturbation function is smooth. By $$\varepsilon $$ ε -regularity and suitable perturbations, we can then show that such a sequence of perturbed $$\alpha $$ α -Dirac-harmonic maps converges to a smooth coupled $$\alpha $$ α -Dirac-harmonic map.

Modulational stability of solitary states in a lossy nonlinear electrical line

2009 ◽  
Vol 87 (11) ◽  
pp. 1191-1202 ◽  
Author(s):  
E. Kengne ◽  
R. Vaillancourt
Keyword(s):  
Eigenvalue Problem ◽  
Growth Rates ◽  
Pulse Propagation ◽  
Landau Equation ◽  
Perturbation Function ◽  
Electrical Transmission ◽  
Ginzburg Landau ◽  
Electrical Transmission Line ◽  
Complex Functions ◽  
Modulational Stability

The modified Ginzburg–Landau equation that describes the pulse propagation in a lossy electrical transmission line is used to derive an eigenvalue problem that allows a detailed investigation of the modulational stability of the solitary states in the line. It is found that the growth rates of the perturbation are complex functions of the spatial variable and that, in general, the solitary states in the network can be either modulationally stable, unstable, or destabilized under a given perturbation function.

Symmetry property of the electric quadrupole perturbation function in gamma ray angular correlations

1990 ◽  
Vol 113 (4) ◽  
pp. 297-302
Author(s):  
S. Connell ◽  
K. Bharuth-Ram ◽  
H. Appel ◽  
J. P. F. Sellschop ◽  
M. Stemmet
Keyword(s):  
Symmetry Property ◽  
Gamma Ray ◽  
Electric Quadrupole ◽  
Perturbation Function ◽  
Angular Correlations

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

2013 ◽  
Vol 11 (5) ◽  
Author(s):  
Liana Cioban ◽  
Ernö Csetnek
Keyword(s):  
Variational Inequalities ◽  
Regularity Condition ◽  
Equilibrium Problems ◽  
Gap Functions ◽  
Conjugate Duality ◽  
Perturbation Function ◽  
General Variational Inequalities ◽  
Necessary And Sufficient ◽  
Convex Subdifferential ◽  
Convex Setting

AbstractBased on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka G., On gap functions for equilibrium problems via Fenchel duality, Pac. J. Optim., 2006, 2(3), 667–678] and [Altangerel L., Boţ R.I., Wanka G., On the construction of gap functions for variational inequalities via conjugate duality, Asia-Pac. J. Oper. Res., 2007, 24(3), 353–371]. By particularizing the perturbation function we rediscover several gap functions from the literature. We also characterize the solutions of various variational inequalities and equilibrium problems by means of the properties of the convex subdifferential. In case no regularity condition is fulfilled, we deliver also necessary and sufficient sequential characterizations for these solutions. Several examples are illustrating the theoretical aspects.

Duality Theory

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Duality Theory ◽  
Dual Problem ◽  
Optimization Problems ◽  
Strong Duality ◽  
Perturbation Function ◽  
Primal Problem ◽  
Theory Section ◽  
Existence Conditions ◽  
Definition Of ◽  
Optimal Multiplier

Nonlinear optimization problems have two different representations, the primal problem and the dual problem. The relation between the primal and the dual problem is provided by an elegant duality theory. This chapter presents the basics of duality theory. Section 4.1 discusses the primal problem and the perturbation function. Section 4.2 presents the dual problem. Section 4.3 discusses the weak and strong duality theorems, while section 4.4 discusses the duality gap. This section presents the formulation of the primal problem, the definition and properties of the perturbation function, the definition of stable primal problem, and the existence conditions of optimal multiplier vectors.

scholarly journals The Reference Frames and a Transformation of the Spherical Functions

1980 ◽  
Vol 56 ◽  
pp. 255-259
Author(s):  
V. G. Shkodrov
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Spherical Functions ◽  
Coordinate Frame ◽  
Perturbation Function ◽  
Solid Bodies

AbstractThe use of spherical functions in dynamical problems is very common. As a rule, they arise in perturbing functions. It is well known that passing from one reference frame to another is accompanied by a double transformation of the perturbation function. That is why problems lose their simplicity and elegance. The problem of two solid bodies is a typical example in this respect.In the present paper the questions connected with the transformation of the spherical functions when passing from one reference frame to another frame are considered. Traditional functions are generally unsuitable as they introduce a series of difficulties in the problems. That is why complex spherical functions are used. The transformation of spherical functions due to rotation of the coordinate frame is made by means of the Wigner’s functions. When translating the frame the Clebsch-Gordon’s coefficients are used.

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