Propagation Of Amplitudes Research Articles

Existence of a regular solution for 1D Green\u2013Naghdi equations with surface tension at a large time instant

In this paper the model 1D-GNσ is considered, which concerns the 1D Green–Naghdi equations with non-flat bottom and under the influence of surface tension, to be widely used in coastal oceanography to describe the propagation of large-wave amplitudes. The purpose of this paper is to show that the solution of 1D-GNσ can be made by the Picard iterative scheme, which proves that there is no loss of regularity of the solution relative to the initial condition.

Travelling-wave amplitudes as solutions of the phase-field crystal equation.

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the [Formula: see text] method (Malfliet & Hereman 1996 Phys. Scr.15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput.154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general [Formula: see text] solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general [Formula: see text] solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

General set of traveling-wave solutions for amplitude equations in the phase field crystal model

Fronts dynamics of periodic crystalline state, which invades the homogeneous state (liquid phase), are analysed. These fronts are considered as traveling waves of atomic density amplitudes. The propagation of amplitudes is described by the hyperbolic equation of an extended Allen-Cahn type for which the complete set of analytical traveling-wave solutions are obtained by tanh-method. The set of solutions includes previously known traveling waves for the parabolic Allen-Cahn equation of both extended and standard form.

Theoretical investigation on nearsightedness of finite model and molecular systems based on linear response function analysis.

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, |r−r′|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems’ counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.

Optical surface modes in the presence of nonlinearity and disorder

We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson-nonlinear Schrödinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.

Improvement of the Internal Consistency in Trajectory Surface Hopping

This paper addresses the issue of internal consistency in the molecular dynamics with quantum transitions (MDQT) surface hopping method. The MDQT method is based on Tully's fewest switches algorithm, which is designed to ensure that the fraction of trajectories on each surface is equivalent to the corresponding average quantum probability determined by coherent propagation of the quantum amplitudes. For many systems, however, this internal consistency is not maintained. Two reasons for this discrepancy are the existence of classically forbidden transitions and the divergence of the independent trajectories. This paper presents a modified MDQT method that improves the internal consistency. The classically forbidden switches are eliminated by utilizing modified velocities for the integration of the quantum amplitudes, and the difficulties due to divergent trajectories are alleviated by removing the coherence of the quantum amplitudes when each trajectory leaves a nonadiabatic coupling region. The standard and modified MDQT methods are compared to fully quantum calculations for a classic model for ultrafast electronic relaxation (i.e., a two-state three-mode model of the conically intersecting S1 and S2 excited states of pyrazine). The standard MDQT calculations exhibit significant discrepancies between the fraction of trajectories in each state and the corresponding average quantum probability. The modified MDQT method leads to remarkable internal consistency for this model system.

Propagation of eigenmodes and transfer amplitudes in optical waveguide structures

A method of transfer amplitudes suitable for modeling and simulation in integrated optical circuits is presented. The method is based on vectorial formulation of electrodynamics: distributions and propagation of electromagnetic fields in optical circuits are described by equivalent surface sources. This approach permits a division of complex optical waveguide structures into sets of primitive blocks and to separately calculate the transfer amplitude for each block. The transfer amplitude of the entire optical system is represented by a convolution of transfer amplitudes of its primitive blocks. Diffraction in slab regions is taken into account using known propagation functions. It is shown that the concept of a normalized transverse eigenfunction of the diffracted field is very useful in calculations of transfer amplitudes. The crucial role of transverse Bloch modes in propagation through multiwaveguide structures is emphasized. With this method, the eigenvalues and eigenfunctions of an arbitrary waveguide structure can be obtained with high accuracy. The general approach is illustrated with the transfer amplitude and efficiency calculations for a star coupler and a waveguide grating router.

Geometro-stochastically quantized fields with internal spin variables

The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry and Kihlberg a four-dimensional internal spin space S̄ is chosen possessing an invariant measure and being able to represent integer as well as half integer spins. S̄ is a homogeneous space of the group SL(2,C) parametrized in terms of spinors α∈C2 and their complex conjugates ᾱ. The generalized scalar quantum mechanical wave functions may be reduced to yield irreducible components of definite physical mass and spin [m,s], with m⩾0 and s=0,12,1,32,… , with spin described in terms of the usual (2s+1)-component fields. Viewed from the internal space description of spin this reduction amounts to a restriction of the variable α to a compact subspace of S̄, i.e., a “spin shell” Sr=2s2 of radius r=2s in C2. This formulation of single particles or single antiparticles of type [m,s] is then used to study the geometro-stochastic (i.e., quantum) propagation of amplitudes for arbitrary spin on a curved background space–time possessing a metric and axial vector torsion treated as external fields. A Poincaré gauge covariant path integral-like representation for the probability amplitude (generalized wave function) of a particle with arbitrary spin is derived satisfying a second order wave equation on the Hilbert bundle constructed over curved space–time. The implications for the stochastic nature of polarization effects in the presence of gravitation are pointed out and the extension to Fock bundles of bosonic and fermionic type is briefly mentioned.

突風学力レベルが疲労き裂進展挙動に及ぼす影響 フライトシミュレーション応力下のき裂進展の加速と遅延

Fatigue tests were carried out on 2024-T3 aluminum alloy sheet material under 11 kinds of flight simulation loadings and its crack propagation behavior was observed. In this experiment, flight simulation loadings were made to simplify a complex stress history so that they consisted of the ground to air cycle of large stress range and gust cycles of relatively small stress range.The results obtained were as follows:(1) When the maximum stress of the ground to air cycle was equal to the maximum stress of gust cycles, the crack propagation rate under flight simulation loading was faster than that estimated by the linear damage law on the basis of crack propagation of constant stress amplitudes.(2) When the maximum stress of gust cycles was 40MPa or 80MPa lower than that of the ground to air cycle, the crack propagation rate in a short crack length was almost the same as the estimated value. With increasing crack length, the crack propagation clearly showed the retardation behavior. As the crack length increased further and approached to the critical value of final fracture, the crack propagation rate gradually recovered to the estimated values.(3) When the maximum stress of gust cycles was 120MPa or 160MPa lower than that of the ground to air cycle, the crack propagation rate under the flight simulation was nearly equal to the estimated value and the retardation behavior could not be observed in the whole range of crack propagation.(4) The retardation behavior of crack propagation was not observed just after changing the stress of the ground to air cycle to the gust stress, but the crack propagation clearly showed the retardation behavior with increasing the number of gust cycles in the same flight.

Multichannel quantum theory for propagation of second order transition amplitudes

We study the Green’s function representation of second order transition amplitudes for the transition from an initial to a final quantum state that occurs because both are weakly coupled to a manifold of intermediate states. These processes apply to Raman scattering, two-photon absorption, fluoresecence from dissociating molecules, electron stimulated desorption, etc., and the transition amplitudes are called generalized Raman amplitudes. The generalized Raman transition amplitudes are expressed in terms of matrix elements of a multichannel Green’s function whose determination requires the simultaneous generation of the regular and irregular solutions of the multichannel Schrödinger equation for the intermediate state manifold. However, the numerical propagation of the generalized Raman transition amplitudes through classically forbidden regions requires, in effect, the simultaneous propagation (in the same direction) of both the regular and irregular solutions of the intermediate manifold Schrödinger equation, and use of standard multichannel scattering methods lead to numerical instabilities. We introduce new methods for maintaining both the stability and linear independence of the regular and irregular multichannel intermediate manifold eigenfunctions as they are one-way propagated along a reaction coordinate with standard quantum scattering methods. The methods may be used with systems having asymptotically open or closed channels or both in the intermediate state manifold. First order transition amplitudes, such as state selected photodissociation amplitudes to fragment states of the intermediate state manifold, emerge as a by-product of our algorithm, and the computation of the second order generalized Raman amplitudes scales roughly as double the computation time required for the first order amplitudes.