Wyniki wyszukiwania - Biblioteka Nauki

1

Simulation of Radiation Effects in SiO₂/Si Structures

100%

Komarov F. , Zayats G. , Komarov A. , Miskiewicz S. , Michailov V. , Komsta H.

Acta Physica Polonica A

|

2015

|

tom 128

|

nr 5

857-860

EN

The space-time evolution of electric charge induced in the dielectric layer of simulated metal-insulator-semiconductor structures due to irradiation with X-rays is discussed. The system of equations used as a basis for the simulation model is solved iteratively by the efficient numerical method. The obtained simulation results correlate well with the respective data presented in other scientific publications.

2

Solutions for Conservative Nonlinear Oscillators Using an Approximate Method Based on Chebyshev Series Expansion of the Restoring Force

80%

Beléndez A. , Hernández A. , Beléndez T. , Pascual C. , Alvarez M. , Arribas E.

Acta Physica Polonica A

|

2016

|

tom 130

|

nr 3

667-678

EN

Approximate solutions for small and large amplitude oscillations of conservative systems with odd nonlinearity are obtained using a "cubication" method. In this procedure, the Chebyshev polynomial expansion is used to replace the nonlinear function by a third-order polynomial equation. The original second-order differential equation, which governs the dynamics of the system, is replaced by the Duffing equation, whose exact frequency and solution are expressed in terms of the complete elliptic integral of the first kind and the Jacobi elliptic function cn, respectively. Then, the exact solution for the Duffing equation is the approximate solution for the original nonlinear differential equation. The coefficients for the linear and cubic terms of the approximate Duffing equation - obtained by "cubication" of the original second-order differential equation - depend on the initial oscillation amplitude. Six examples of different types of common conservative nonlinear oscillators are analysed to illustrate this scheme. The results obtained using the cubication method are compared with those obtained using other approximate methods such as the harmonic, linearized and rational balance methods as well as the homotopy perturbation method. Comparison of the approximate frequencies and solutions with the exact ones shows good agreement.

3

Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations

80%

Aslan İ.

Acta Physica Polonica A

|

2013

|

tom 123

|

nr 1

16-20

EN

Nonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.

4

Response of Superconductor Bolometer to Phonon Fluxes

80%

Danilchenko B. , Jasiukiewicz C. , Paszkiewicz T. , Wolski S.

Acta Physica Polonica A

|

2003

|

tom 103

|

nr 4

325-338

EN

A metallic film bolometer with heat capacity C is in contact with thermal bath and with crystalline specimen and is biased by a constant current I_b. The thermal contact of the bolometer is characterized by the thermal conductance G. The bolometer operates in the linear regime of dependence of resistance on temperature characterized by a constantα. Experiments which allow one to measureα, C, and G are proposed. The characteristic timeτ=C/G and characteristic current I_m=√{G/α} affect the effective relaxation rateΛ of the bolometer resistance R_b(t). The knowledge of the power W(t) absorbed by detector allows one to calculate R_b(t). The inverse problem of calculation of W(t) from known R_b(t) is also solved. The suitable algorithms are proposed. Deconvoluted absorbed power is obtained for experiments performed on GaAs and compared with phonoconductivity signal of two-dimensional electron gas structure as well as with results of Monte Carlo computer experiments.

5

The Method of Jacobi Last Multiplier for Integrating Nonholonomic Systems

80%

Zhang Y.

Acta Physica Polonica A

|

2011

|

tom 120

|

nr 3

443-446

EN

In this paper, a new integral method of nonholonomic dynamical systems is put forward. The differential equations of motion of nonholonomic systems in phase space are established. The definition of the Jacobi last multiplier of the systems is given, and the relation between the Jacobi last multiplier and the first integrals of the systems is discussed. The researches show that the solution of the systems can be found by the last multiplier if the quantity of first integrals of the systems is sufficient. An example is given to illustrate the application of the results.

6

Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube

80%

Yayli M.

Acta Physica Polonica A

|

2015

|

tom 127

|

nr 3

678-683

EN

This paper presents an analytical formulation of nonlocal elasticity theory for the buckling analysis of simply supported carbon nanotubes with rotational springs at both ends. The lateral displacement function is represented by a Fourier sine series expansion. Stoke's transformation is applied to construct the coefficient matrix of the corresponding systems of linear equations. This matrix gives more flexibility in boundary conditions. The accuracy of proposed method is validated for three well-known boundary conditions available in the literature. A very good agreement has been obtained. The present method permits to have more efficient stability matrix for calculating the buckling loads of carbon nanotubes with any desired boundary conditions.

7

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

80%

Evirgen F.

Acta Physica Polonica A

|

2017

|

tom 132

|

nr 3

1062-1065

EN

In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system.

8

Laguerre Polynomial Solutions of a Class of Initial and Boundary Value Problems Arising in Science and Engineering Fields

80%

Gürbüz B. , Sezer M.

Acta Physica Polonica A

|

2016

|

tom 130

|

nr 1

194-197

EN

In this study, we consider high-order nonlinear ordinary differential equations with the initial and boundary conditions. These kinds of differential equations are essential tools for modelling problems in physics, biology, neurology, engineering, ecology, economy, astrophysics, physiology and so forth. Each of the mentioned problems are described by one of the following equations with the specific physical conditions: Riccati, Duffing, Emden-Fowler, Lane Emden type equations. We seek the approximate solution of these special differential equations by means of a operational matrix technique, called the Laguerre collocation method. The proposed method is based on the Laguerre series expansion and the collocation points. By using the method, the mentioned special differential equations together with conditions are transformed into a matrix form which corresponds to a system of nonlinear algebraic equations with unknown Laguerre coefficients, and thereby the problem is approximately solved in terms of Laguerre polynomials. In addition, some numerical examples are presented to demonstrate the efficiency of the proposed method and the obtained results are compared with the existing results in literature.

9

An Explicit Analytic Solution to the Thomas-Fermi Equation by the Improved Differential Transform Method

70%

Fatoorehchi H. , Abolghasemi H.

Acta Physica Polonica A

|

2014

|

tom 125

|

nr 5

1083-1087

EN

In this paper, a newly proposed analytical scheme by the authors namely the improved differential transform method is employed to provide an explicit series solution to the Thomas-Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with differentiation, and ends up in a recursive formula involving the Adomian polynomials to afford the unknown coefficients. Unlike many other methods, our approach is free of integration and hence can be of computational interest. In addition, a very good agreement between the proposed solution and the results from several well-known works in the literature is demonstrated.

10

Analytic Approximations for Thomas-Fermi Equation

70%

El-Nahhas A.

Acta Physica Polonica A

|

2008

|

tom 114

|

nr 4

913-918

EN

In this paper, we give an analytic approximation to the solution of the Thomas-Fermi equation using the homotopy analysis method and with the use of a polynomial exponential basis.

11

Romanovski polynomials in selected physics problems

51%

Raposo A. , Weber H. , Alvarez-Castillo D. , Kirchbach M.

Open Physics

|

2007

|

tom 5

|

nr 3

253-284

EN

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.