Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

2003 ◽  
Vol 28 (9) ◽  
pp. 722 ◽  
Author(s):  
Wei-Ping Zang ◽  
Jian-Guo Tian ◽  
Zhi-Bo Liu ◽  
Wen-Yuan Zhou ◽  
Chun-Ping Zhang ◽  
...  
Keyword(s):  
Variational Method ◽  
Nonlinear Absorption ◽  
Beam Propagation ◽  
Numerical Results ◽  
Kerr Medium

The Elastic Moduli of Fiber-Reinforced Materials

1964 ◽  
Vol 31 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Zvi Hashin ◽  
B. Walter Rosen
Keyword(s):  
Variational Method ◽  
Cross Sections ◽  
Elastic Moduli ◽  
Numerical Results ◽  
Exact Results ◽  
Effective Elastic Moduli ◽  
Fiber Reinforced ◽  
Random Array ◽  
Fiber Reinforced Materials ◽  
Hexagonal Arrays

Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal arrays of identical fibers and approximate results for random array of fibers, which may have unequal cross sections. Typical numerical results have been obtained for technically important elastic moduli.

POLARON CORRECTION TO THE NEGATIVE DONOR ON THE HETERO-INTERFACE IN MAGNETIC FIELDS (II–VI CRYSTALS)

2003 ◽  
Vol 17 (31n32) ◽  
pp. 6097-6107 ◽  
Author(s):  
XIAOYAN ZHANG ◽  
XU WANG ◽  
GUOLIANG FAN
Keyword(s):  
Magnetic Fields ◽  
Variational Method ◽  
Triplet State ◽  
Numerical Results ◽  
Binding Energies ◽  
Phonon Coupling ◽  
Polar Crystal ◽  
Spin Triplet

Negative donor ion on the hetero-interface in magnetic fields are investigated. Using a variational method, we have calculated the binding energies of D- center for the spin-triplet state of L=-1 in this structure. Moreover, the effect of electron-interface phonon coupling on the energy of a donor located in a polar-crystal hetero-interface is found. Numerical results are produced for heterostructures of some II–VI crystals.

DECOHERENCE OF THE TRIANGULAR BOUND POTENTIAL QUANTUM DOT QUBIT

2009 ◽  
Vol 23 (27) ◽  
pp. 3273-3279 ◽  
Author(s):  
JIA-KUI SUN ◽  
HONG-JUAN LI ◽  
JING-LIN XIAO
Keyword(s):  
Quantum Dot ◽  
Variational Method ◽  
Excited States ◽  
Polar Angle ◽  
Numerical Results ◽  
Coupling Constant ◽  
Phonon Coupling ◽  
Strongly Coupled ◽  
Decoherence Rate ◽  
Triangular Bound Potential

We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Our numerical results indicate that the decoherence rate will decrease with increasing the confinement length of the quantum dot (QD) and decrease with increasing electron-LO-phonon coupling constant. The influences of the polar angle on the decoherence rate are dominant when the coupling constant increases, while the effects of the polar angle on that are strong when the confinement length increases. Meanwhile, the decoherence rate varies periodically with respect to the polar angle.

scholarly journals Increasing regularity of generalized solutions to the wave equation for computing optimal boundary controls

2016 ◽  
pp. 299-308
Author(s):  
Д.А. Иванов
Keyword(s):  
Wave Equation ◽  
Variational Method ◽  
Numerical Results ◽  
Generalized Solutions ◽  
Optimal Boundary ◽  
Phase Trajectories ◽  
Boundary Controls ◽  
Stable Approximation

Для волнового уравнения на промежутках докритической длины рассмотрены задачи с двусторонними граничными управлениями трех основных типов в классах слабых обобщенных решений. Для устойчивого приближенного вычисления граничных управлений предложен метод, основанный на предварительном сглаживании фазовых траекторий, применении вариационного метода в классах сильных обобщенных решений и финальном дифференцировании найденных сглаженных управлений. Приведены вычислительные иллюстрации. Problems with two-sided boundary controls of three main types are considered for the wave equation in the classes of weak generalized solutions on intervals of subcritical length. An algorithm is proposed for the stable approximation of boundary controls. This algorithm is based on the preliminary smoothing of phase trajectories, the application of a variational method in the classes of strong generalized solutions, and the final differentiation of the resulting smoothed controls. Numerical results are discussed.

Transverse instability of soliton solutions to nonlinear Schrödinger equations

1979 ◽  
Vol 21 (2) ◽  
pp. 259-266 ◽  
Author(s):  
D. Anderson ◽  
A. Bondeson ◽  
M. Lisak
Keyword(s):  
Variational Method ◽  
Growth Rates ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Numerical Results ◽  
Transverse Instability ◽  
Exponential Nonlinearity ◽  
Nonlinear Schrödinger ◽  
Good Agreement ◽  
Explicit Expressions

An inverstigation is made of the transverse instability of plane soliton solutions of the nonlinear Schrödinger equation, including the case of an exponential nonlinearity. The analysis is based on a variational method, where specific trial functions are applied for the perturbations. Explicit expressions for the growth rates are given, showing good agreement with numerical results.

CONFINED LENNARD–JONES POTENTIAL: A VARIATIONAL TREATMENT

2010 ◽  
Vol 25 (08) ◽  
pp. 641-648 ◽  
Author(s):  
F. R. SILVA ◽  
E. DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Energy Levels ◽  
Numerical Results ◽  
Supersymmetric Quantum Mechanics ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Energy Eigenvalues ◽  
Lennard Jones ◽  
Variational Treatment

In this work, the energy eigenvalues for the confined Lennard–Jones potential are calculated through the Variational Method allied to the Supersymmetric Quantum Mechanics. Numerical results are obtained for different energy levels, parameters of the potential and values of confinement radius. In the limit, where this radius assumes great values, the results for the non-confined case are recovered.

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