The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use...
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The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. ''Counting lemmas'' for the non-selfadjoint operator L, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite disc D in the complex eigenvalue plane. The radius of the disc D is controlled by the H-1 norm of the potential q. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds - ''whiskered tori'' for the NLS pde. The Floquet discriminant DELTA(lambda;q) used to introduce a natural sequence of NLS constants of motion, [F(j)(q) = DELTA(lambda = lambda(j)c(q);q), where lambda(j)c denotes the j(th) critical point of the Floquet discriminant DELTA(lambda)]. A Taylor series expansion of the constants F(j)(q), with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of F(j)(q), which themselves are expressed in terms of quadratic products of eigenfunctions of L. The second variation permits identification, within the disc D, of important bifurcations m the spectral configurations of the operator L. The constant F(j)(q), as the height of the Floquet discriminant over the critical point lambda(j)c, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, {F(j)(q)}\j\>N, which is associated with critical points outside the disc D. Within this disc, the interpretation is only valid locally, with the s
In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spheri...
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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.
Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this note, the homoclinic orbits of the doubly periodic Davey-Stewartson equation are obtained by using the Hirota's bilin...
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Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this note, the homoclinic orbits of the doubly periodic Davey-Stewartson equation are obtained by using the Hirota's bilinear methods, which is important to the study on the global property of the doubly periodic Davey-Stewartson equation.
Majorana's stellar representation provides an intuitive picture in which quantum states in highdimensional Hilbert space can be observed using the trajectory of Majorana *** consider the Majorana's stellar rep...
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Majorana's stellar representation provides an intuitive picture in which quantum states in highdimensional Hilbert space can be observed using the trajectory of Majorana *** consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/*** real and imaginary parts of the quantum geometric tensor,corresponding to the quantum metric tensor and Berry curvature,are therefore obtained in terms of the Majorana ***,we work out the expressions of quantum geometric tensor for arbitrary spin in some important *** results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.
In this paper, we study the decay rates of the generalized Benjamin-Bona-Mahony equations in n-dimensional space. By using Fourier analysis for long wave and by applying the energy method for short wave, we obtain the...
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In this paper, we study the decay rates of the generalized Benjamin-Bona-Mahony equations in n-dimensional space. By using Fourier analysis for long wave and by applying the energy method for short wave, we obtain the Hm convergence rates of the solutions when the initial data are in the bounded subset of the phase space HmeRnTen P 3T. The optimal decay rates are obtained in our results and are found to be the same as the Heat equation.
A non-relativistic description of the differential cross section (DCS) for Thomas double-scattering electron capture at asymptotically high velocity is developed within the third-order continuum distorted-wave (CDW) p...
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A non-relativistic description of the differential cross section (DCS) for Thomas double-scattering electron capture at asymptotically high velocity is developed within the third-order continuum distorted-wave (CDW) perturbation theory for 1s --> 1s transitions in proton-hydrogen collisions. It is shown that at the critical proton scattering angles, namely the forward peak, Thomas maximum, small angles and the interference minimum, the CDW series has converged at second order. Moreover, it is proven that the third-order correction makes no contribution to the velocity-dependent upsilon-(11) and upsilon-(12) behaviour of the Thomas double-scattering total cross sections at the leading angles. The Oppenheimer-Brinkman-Kramers (OBK) travelling atomic orbital plane wave theory is compared to the CDW approximation. It is observed that the second-order OBK (OBK2) theory has not converged. It remains an open question as to whether fourth-order terms or higher in the OBK approximation contribute to the various differential cross sections. It is concluded that the CDW model gives a superior description of the Thomas double-scattering mechanism than the OBK model.
Numerical results for the Nikitin exponential model at non-zero impact parameters are presented. It is confirmed that in order to derive the correct strong-coupling approximation of the transition probability, one nee...
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Numerical results for the Nikitin exponential model at non-zero impact parameters are presented. It is confirmed that in order to derive the correct strong-coupling approximation of the transition probability, one need only include the leading terms of the asymptotic expansions of the confluent hypergeometric functions. Development beyond leading order is inappropriate to the particular model, because by construction the non-analytic wavefunction is discontinuous in its second-order derivative at the turning point, which follows from the cusp-like discontinuity in the first-order derivative of at least the off-diagonal Hamiltonian potential matrix elements. It is therefore concluded that the Stueckelberg phase-integral derivations of Crothers are essential if transition probabilities and cross sections are not to be underestimated at large impact parameters, due to neglecting the bending of the double Stokes line.
Superionic ices with highly mobile protons within stable oxygen sub-lattices occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the *** the thermal...
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Superionic ices with highly mobile protons within stable oxygen sub-lattices occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the *** the thermal transport in superionic ice is vital for the thermal evolution of icy ***,it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons,beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics *** utilizing the deep potential molecular dynamics approach,we investigate the thermal conductivity of ice-Ⅶ and superionic ice-Ⅶ’’ along the isobar of P = 30 GPa.A non-monotonic trend of thermal conductivity with elevated temperature is *** heat flux decomposition and trajectory-based spectra analysis,we show that the thermally activated proton diffusion in ice-Ⅶ and superionic ice-Ⅶ′′contribute significantly to heat convection,while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat *** competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in *** work unravels the important role of proton diffusion in the thermal transport of high-pressure *** approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials.
In this paper, the global existence of classical solution and global attractor for Camassa-Holm type equations with dissipative term are established by using fixed point theorem and a priori estimates.
In this paper, the global existence of classical solution and global attractor for Camassa-Holm type equations with dissipative term are established by using fixed point theorem and a priori estimates.
By molecular dynamics simulations employing an embedded atom model potential, we investigate the fcc-to-bcc phase transition in single crystal Al, caused by uniform compression. Results show that the fcc structure is ...
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By molecular dynamics simulations employing an embedded atom model potential, we investigate the fcc-to-bcc phase transition in single crystal Al, caused by uniform compression. Results show that the fcc structure is unstable when the pressure is over 250 GPa, in reasonable agreement with the calculated value through the density flmctional theory. The morphology evolution of the structural transition and the corresponding transition mechanism are analysed in detail. The bcc （011） planes are transited from the fcc （111） plane and the （111） plane. We suggest that the transition mechanism consists mainly of compression, shear, slid and rotation of the lattice. In addition, our radial distribution flmction analysis explicitly indicates the phase transition of Al from fee phase to bce structure.
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