The Experts below are selected from a list of 13134 Experts worldwide ranked by ideXlab platform

Yong Chen - One of the best experts on this subject based on the ideXlab platform.

  • localized excitations and interactional solutions for the reduced maxwell Bloch Equations
    Communications in Nonlinear Science and Numerical Simulation, 2019
    Co-Authors: Lili Huang, Yong Chen
    Abstract:

    Abstract Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell–Bloch Equations. The nonlocal symmetries of the reduced Maxwell–Bloch Equations are obtained by the truncated Painleve expansion approach and the Mobious invariant property. The nonlocal symmetries are localized to a prolonged system by introducing suitable auxiliary dependent variables. The extended system can be closed and a novel Lie point symmetry system is constructed. By solving the initial value problems, a new type of finite symmetry transformations is obtained to derive periodic waves, Ma breathers and breathers travelling on the background of periodic line waves. Then rich exact interactional solutions are derived between solitary waves and other waves including cnoidal waves, rational waves, Painleve waves, and periodic waves through similarity reductions. In particular, several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction. By computer numerical simulation, the dynamics of these localized excitations and interactional solutions are discussed, which exhibit meaningful structures.

  • Soliton–cnoidal interactional wave solutions for the reduced Maxwell–Bloch Equations*
    Chinese Physics B, 2018
    Co-Authors: Lili Huang, Zhijun Qiao, Yong Chen
    Abstract:

    In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch Equations. The truncated Painleve analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch Equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form. Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch Equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.

  • soliton cnoidal interactional wave solutions for the reduced maxwell Bloch Equations
    Chinese Physics B, 2018
    Co-Authors: Lili Huang, Zhijun Qiao, Yong Chen
    Abstract:

    In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch Equations. The truncated Painleve analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch Equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form. Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch Equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.

Xudong Chen - One of the best experts on this subject based on the ideXlab platform.

  • ensemble observability of Bloch Equations with unknown population density
    Automatica, 2020
    Co-Authors: Xudong Chen
    Abstract:

    Abstract We introduce in the paper a novel observability problem for a large population (in the limit, a continuum ensemble) of nonholonomic control systems with unknown population density. We address the problem by focussing on a prototype, namely, the ensemble of Bloch Equations which is known for its use of describing the evolution of the bulk magnetization of a collective of non-interacting nuclear spins in a static field modulated by a radio frequency (rf) field. The dynamics of the Equations are structurally identical, but show variations in Larmor dispersion and rf inhomogeneity. We assume that the initial state of any individual system (i.e., individual Bloch equation) is unknown and, moreover, the population density of these individual systems is also unknown. Furthermore, we assume that at any time, there is only one scalar measurement output at our disposal. The measurement output integrates a certain observation function, common to all individual systems, over the continuum ensemble. The observability problem we pose in the paper is thus the following: Whether one is able to use the common control input (i.e., the rf field) and the single measurement output to estimate both the initial states of the individual systems and the population density? Amongst other things, we establish a sufficient condition for the ensemble system to be observable: We show that if the common observation function is any harmonic homogeneous polynomial of positive degree, then the ensemble system is observable. The proof of the result utilizes tools from representation theory of Lie algebras. Although the results established in the paper are for the specific ensemble of Bloch Equations, the approach developed along the analysis can be generalized to investigate observability of other ensemble systems with single, integrated measurement outputs.

  • ensemble observability of Bloch Equations with unknown population density
    arXiv: Systems and Control, 2019
    Co-Authors: Xudong Chen
    Abstract:

    We introduce in the paper a novel observability problem for a continuum ensemble of nonholonomic control systems with unknown population density. We address the problem by focussing on a prototype of such ensemble system, namely, the ensemble of Bloch Equations. The dynamics of the Equations are structurally identical, but show variations in Larmor dispersion and radio frequency (rf) inhomogeneity. We assume that the initial state of every individual system is unknown and, moreover, the population density of these individual systems is also unknown. Furthermore, we assume that at any time, there is only one scalar measurement output at our disposal. The measurement output integrates a certain observation function, common to all individual systems, over the continuum ensemble. The observability problem we pose in the paper is thus the following: Whether one is able to use the common control input (i.e., the rf field) and the single measurement output to estimate the initial states of the individual systems and, moreover, to identify the population density? Amongst other things, we establish a sufficient condition for the ensemble system to be observable: We show that if the common observation function is any harmonic homogeneous polynomial of positive degree, then the ensemble system is observable. The main focus of the paper is to demonstrate how to leverage tools from representation theory of Lie algebras to address the observability problem. Although the results we establish in the paper are for the specific ensemble of Bloch Equations, the approach we develop along the analysis can be generalized to investigate observability of other general ensembles of nonholonomic control systems with a single, integrated measurement output.

Jochen Rau - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Bloch Equations for a strongly driven tunneling system
    Physical Review E, 1997
    Co-Authors: Peter Neu, Jochen Rau
    Abstract:

    Using the Robertson projection operator formalism, we derive generalized Bloch Equations which describe the dynamics of a biased two-level tunneling system strongly driven by an external field and weakly coupled to a super-Ohmic heat bath. The generalized Bloch Equations constitute a set of coupled nonlinear integro-differential Equations. With their help we investigate the influence of phonons on the phenomenon of dynamical localization.

David E. Rourke - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Resolution and Inversion of the Bloch Equations with Relaxation
    Letters in Mathematical Physics, 2007
    Co-Authors: Alexander A. Karabanov, David E. Rourke
    Abstract:

    It is demonstrated that the linear Bloch Equations, describing near-resonant excitation of two-level media with relaxation, can be resolved into a 3 n -dimensional nonlinear system associated with a special spectral problem, generalizing the classical Zakharov–Shabat spectral problem. Remarkably, for n = 1 it is the well-known Lorenz system, and for n > 1 several such systems coupled with each other in a manner dependant on the excitation pulse. The unstable manifold of a saddle equilibrium point in this ensemble characterizes possible excitations of the spins from the initial equilibrium state. This enables us to get a straightforward geometric extension of the inverse scattering method to the damped Bloch Equations and hence invert them, i.e., design frequency selective pulses automatically compensated for the effect of relaxation. The latter are essential, for example, in nuclear magnetic resonance and extreme nonlinear optics.

  • The Bloch Equations when T1 = T2
    Inverse Problems, 2007
    Co-Authors: David E. Rourke, Alexander Karabanov, George H Booth, Ilya Frantsuzov
    Abstract:

    The Bloch Equations with relaxation times equal, i.e., T1 = T2, can be reduced to the spinor equation of motion (or Zakharov?Shabat eigenvalue problem). The response to a complex, time-varying driving field can be expressed essentially as a Laplace transform of the solution to the spinor equation. This enables, in many cases, closed-form expressions for the response to be obtained, when closed-form solutions exist for the corresponding spinor equation. It enables the 'inversion' of the Bloch Equations to produce relaxation-selective driving fields, i.e., the calculation of the driving field needed to produce a target response, specified as a function of relaxation rate.

Lili Huang - One of the best experts on this subject based on the ideXlab platform.

  • localized excitations and interactional solutions for the reduced maxwell Bloch Equations
    Communications in Nonlinear Science and Numerical Simulation, 2019
    Co-Authors: Lili Huang, Yong Chen
    Abstract:

    Abstract Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell–Bloch Equations. The nonlocal symmetries of the reduced Maxwell–Bloch Equations are obtained by the truncated Painleve expansion approach and the Mobious invariant property. The nonlocal symmetries are localized to a prolonged system by introducing suitable auxiliary dependent variables. The extended system can be closed and a novel Lie point symmetry system is constructed. By solving the initial value problems, a new type of finite symmetry transformations is obtained to derive periodic waves, Ma breathers and breathers travelling on the background of periodic line waves. Then rich exact interactional solutions are derived between solitary waves and other waves including cnoidal waves, rational waves, Painleve waves, and periodic waves through similarity reductions. In particular, several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction. By computer numerical simulation, the dynamics of these localized excitations and interactional solutions are discussed, which exhibit meaningful structures.

  • Soliton–cnoidal interactional wave solutions for the reduced Maxwell–Bloch Equations*
    Chinese Physics B, 2018
    Co-Authors: Lili Huang, Zhijun Qiao, Yong Chen
    Abstract:

    In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch Equations. The truncated Painleve analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch Equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form. Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch Equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.

  • soliton cnoidal interactional wave solutions for the reduced maxwell Bloch Equations
    Chinese Physics B, 2018
    Co-Authors: Lili Huang, Zhijun Qiao, Yong Chen
    Abstract:

    In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch Equations. The truncated Painleve analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch Equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form. Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch Equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.