An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Interactions between kinetic and radiative processes inside moving absorbing fluids

The aim of this paper is to present several features of the couplings occurring between radiative transfer and the kinetics of a moving dielectric. After determining how the velocity field affects the apparent thermo-optical properties of matter, the energy transport problem is investigated in instationary regime and the general form of transient radiative transfer equation inside a moving medium is built. Then, the model is applied to the particular case of turbulent flows: a system of two equations for mean and fluctuating radiative energies is presented, and the resolution of this system is finally carried out.     

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

A study of the rate-controlled constrained-equilibrium dimension reduction method and its different implementations

The Rate-Controlled Constrained-Equilibrium (RCCE) method is a thermodynamic based dimension reduction method which enables representation of chemistry involving n _s species in terms of fewer n _r constraints. Here we focus on the application of the RCCE method to Lagrangian particle probability density function based computations. In these computations, at every reaction fractional step, given the initial particle composition (represented using RCCE), we need to compute the reaction mapping, i.e. the particle composition at the end of the time step. In this work we study three different implementations of RCCE for computing this reaction mapping, and compare their relative accuracy and efficiency. These implementations include: (1) RCCE/TIFS (Trajectory In Full Space): this involves solving a system of n _s rate-equations for all the species in the full composition space to obtain the reaction mapping. The other two implementations obtain the reaction mapping by solving a reduced system of n _r rate-equations obtained by projecting the n _s rate-equations for species evaluated in the full space onto the constrained subspace. These implementations include (2) RCCE: this is the classical implementation of RCCE which uses a direct projection of the rate-equations for species onto the constrained subspace; and (3) RCCE/RAMP (Reaction-mixing Attracting Manifold Projector): this is a new implementation introduced here which uses an alternative projector obtained using the RAMP approach. We test these three implementations of RCCE for methane/air premixed combustion in the partially-stirred reactor with chemistry represented using the n _s=31 species GRI-Mech 1.2 mechanism with n _r=13 to 19 constraints. We show that: (a) the classical RCCE implementation involves an inaccurate projector which yields large errors (over 50%) in the reaction mapping; (b) both RCCE/RAMP and RCCE/TIFS approaches yield significantly lower errors (less than 2%); and (c) overall the RCCE/TIFS approach is the most accurate, efficient (by orders of magnitude) and robust implementation.     

准方波脉冲形成网络的理论分析与设计

针对微波驱动源、固态调制器等对宽平顶脉冲源的应用需求,开展了基于脉冲形成网络输出准方波的理论研究与分析设计。首先采用Prony算法获得准方波波形的解析表达式,然后基于最佳一致逼近的优化控制思路,列出极点控制方程,采用数值方法求解非线性方程组,获得优化波形参数。在此基础上采用阻抗函数匹配的算法求解出脉冲形成网络的元件参数初始值,根据工程设计的实际情况舍弃部分参数并对个别参数进行优化后,获得最终的元器件参数。通过理论分析与数值模拟相结合的方法,系统地给出了获取长脉宽、低纹波准方波脉冲形成网络的设计方法以及设计准则。该方法可用于设计任意阶低纹波系数的准方波脉冲源,也可用于设计其他输出波形要求的脉冲源。     

An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

Productions of X(1835) as baryonium with sizable gluon content

X(1835) has been treated as a baryonium with sizable gluon content, and to be almost flavor singlet. This picture allows us to rationally understand X(1835) production in J/ψ radiative decays, and its large couplings with pˉ, η^′ππ. The processes ϒ(1S) → γX(1835) and J/ψ → ωX(1835) have been examined. It has been found that Br(ϒ(1S) → γX(1835))Br(X(1835) → pˉ) < 6.45×10^-7, which is compatible with CLEO's recent experimental result (Phys. Rev. D 73, 032001 (2006) hep-ex/0510015). The branching fractions Br(J/ψ → ωX(1835)), Br(J/ψ → ρX(1835)) with X(1835) → pˉ and X(1835) → η^′π⁺π^- have been estimated by the quark-pair creation model. We show that they are heavily suppressed, so the signal of X(1835) is very difficult, if not impossible, to be observed in these processes. The experimental checks for these estimations are expected. The existence of the baryonium nonet is conjectured, and a model-independent derivation of their production branching fractions is presented.     

Reduction of Vaisman structures in complex and quaternionic geometry

We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair $(K,\Gamma )$, where $K$ is a Kähler manifold and $\Gamma$ is a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kähler manifold $(K,\Gamma )$ as the rank of a natural quotient of $\Gamma$, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kähler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover, we define locally conformal hyperKähler reduction as an equivariant version of hyperKähler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally, we show that locally conformal hyperKähler reduction induces hyperKähler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperKähler reduction.