Terms Of Gain Loss Research Articles

Energies of the static solitary wave solutions of the one-dimensional Gross-Pitaevskii equation

We calculated the energies of the static solitary wave solutions of the one-dimensional Gross-Pitaevskii equation with the time-dependent parabolic trap, the time-dependent scattering wave length of s-wave, and the time-dependent external potential describing a gain or loss term. Some written solutions of the equation were used, two of which are based on the experimental results. The solutions satisfy the condition of solitary wave solution since they are localized over the space. By this argument, the energies were obtained by integrating the Hamiltonian density over the space formulated in the classical field theory. To do that, we constructed the appropriate Lagrangian density representing the equation by initially writing the ansatz Lagrangian density and then substituting into the Euler-Lagrange equation. We found that two of the solutions have the same energies and the other one should mathematically have the pure imaginary function describing the gain-loss term to achieve the real energy.

Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media.

We introduce a model based on the one-dimensional nonlinear Schrödinger equation with critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate that a family of solitons, which are unstable in this setting against the critical or supercritical collapse, is stabilized by pinning to an attractive defect, that may also include a parity-time (PT)-symmetric gain-loss component. The model can be realized as a planar waveguide in nonlinear optics, and in a super-Tonks-Girardeau bosonic gas. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact analytical form. In the absence of the gain-loss term, the solitons' stability is investigated in an analytical form too, by means of the Vakhitov-Kolokolov criterion; in the presence of the PT-balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic (critical) medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity. A weak gain-loss component gives rise to intricate alternations of stability and instability in the system's parameter plane. Those solitons which are unstable under the action of the supercritical self-attraction are destroyed by the collapse. On the other hand, if the self-attraction-driven instability is weak and the gain-loss term is present, unstable solitons spontaneously transform into localized breathers, while the collapse does not occur. The same outcome may be caused by a combination of the critical nonlinearity with the gain and loss. Instability of the solitons is also possible when the PT-symmetric gain-loss term is added to the subcritical nonlinearity. The system with self-repulsive nonlinearity is briefly considered too, producing completely stable families of pinned localized states.

Improving information - a necessity in substantiating the accounting decision

As regards the decision-making process, there are two general principles accepted in decision-making: 1) the decision is made in terms of gain-loss; 2) a decision depends on the context; even if the decision-making rules are known, the context of the decision may be different, which means that the meaning of the concepts involved in the decision-making rules changes. The article attempts to introduce the idea that the specification of rules and constraints of concept use should be part of the level of knowledge modeling on the principle of data level separation of the logical level of the application. Specifying constraints at the place and time of manifestation of their knowledge characterizes the context and adapts the decision model. The article addresses the issue of interest and presents examples of accounting.

Bright Solitons in aPT-Symmetric Chain of Dimers

We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.

Deuterium–tritium catalytic reaction in fast ignition: Optimum parameters approach

One of the main concerns about the current working on nuclear power reactors is the potential hazard of their radioactive waste. There is hope that this issue will be reduced in next generation nuclear fusion power reactors. Reactors will release nuclear energy through microexplosions that occur in a mixture of hydrogen isotopes of deuterium and tritium. However, there exist radiological hazards due to the accumulation of tritium in the blanket layer. A catalytic fusion reaction of DTx mixture may stand between DD and an equimolar DT approach in which the fusion process continues with a small amount of tritium seed. In this paper, we investigate the possibility of DTx reaction in the fast ignition (FI) scheme. The kinematic study of the main mechanism of the energy gain–loss term, which may disturb the ignition and burn process, was performed in FI and the optimum values of precompressed fuel and proton beam driver were derived. The recommended values of fuel parameters are: areal density ρR ≥ 5g · cm−2 and initial tritium fraction x ≤ 0.025. For the proton beam, the corresponding optimum interval values are proton average energy 3 ≤ Ep ≤ 10 MeV, pulse duration 5 ≤ tp ≤ 15 ps and power 5 ≤ Wp ≤ 12 × 1022 (keV·cm3 · ps−1). It was proved that under the above conditions, a fast ignition DTx reaction stays in the catalytic regime.

CORRECTION OF THE GROUND STATE ENERGY OF ONE-DIMENSIONAL GROSS-PITAEVSKII EQUATION WITH GAIN-LOSS TERM

We consider the correction of ground state energy of one-dimensional Gross-Pitaevskii equation by adding a gain-loss term as a time-dependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapse-revival of the condensate in the Bose-Einstein condensation. In the Bose-Einstein condensation itself, the function can represent that condensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing an ansatz solution of the wave function and its solution can be dark or bright soliton. Since the Gross-Pitaevskii equation can be treated as a macroscopic quantum oscillator, we can use time-dependent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, time-dependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary one-dimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics.

MEMS 2-Bit Phase-Shifter Failure Mode and Reliability Considerations for Large>tex<$X$>/tex<-Band Arrays

RF microelectromechanical systems (MEMS) switch technology used in the fabrication of phase-shifter circuits is examined from the perspective of failure mode and reliability implications on the performance of large X-band array antennas. Amplitude and phase-state failure probability density functions (pdfs) conditioned on switch probability of failure are formulated for both the hybrid-T (switched line) and coupled-line phase-shifter circuit topologies. The pdfs are used to assess the phase-shifter failure impact on overall array level performance in terms of gain loss and the increase in RMS sidelobe level. Reliability and lifetime implications are addressed through considering a probability of switch failure that increases with cycling. The phase-shifter lifetime switching considerations are related to radar system lifetime beam switching requirements consistent with plausible radar system applications. The key findings are that RF MEMS switch mean time to failure /spl sim/125000 h or longer, consistent with /spl sim/100-125 phase-shifter state switches per second (/spl sim/10/sup 11/ switch operations), are reasonable expectations for RF MEMS phase-shifter technology to meet in order to be considered viable for a broad range of array antenna applications.

On single-mode injection laser structures for reduced output fluctuations

This paper explores the possibilities of two principles for reducing the fluctuations in power output of the main mode of an injection laser: 1) including within the laser cavity a section of larger bandgap than the energy of the photons generated; and 2) use of very small wavelength-selective loss differences between the main mode and the side modes. Transient response and steady-state fluctuations are calculated from a rate-equation model. New approximate analytical expressions are given to make possible the calculation of 1) the critical gain-loss term and 2) the consequent laser characteristics. It is shown that a very small side-mode loss difference increases the coupling between the carrier density and the main-mode photons. This produces very fast transient response. It is also shown that the larger bandgap region smoothens the output power and enhances the main-mode power at constant driving current. These results give promise of a low-power-level laser capable of multigigabit direct modulation