Amplification mechanism of perturbation energy in controlled backward-facing step flow

A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust the amplification rate of the perturbation energy.The amplification mechanisms are investigated numerically via analyzing the characteristics of the terms in the Reynolds-Orr equation which describes the growth rate of the perturbation energy.The results demonstrate that the main convective term always promotes the increase in the growth rate while the viscous terms usually play the reverse role.The contours of the product of the wall-normalwise and streamwise perturbation velocities distribute on both sides of the isoline,which represents the zero wall-normalwise gradient of the streamwise velocity in the base flow,due to the Kelvin-Helmholtz(KH)instability.For the case without control,the isoline downstream the reattachment point of the primary separation bubble is closer to the lower wall,and thus the viscous term near the lower wall might suppress the amplification rate.For the case in which the body force only acts on the secondary separation bubble,the secondary separation bubble is removed,and the magnitude of the negative wall-normalwise gradient of the base flow streamwise velocity decreases along the streamwise direction,and thus the growth rate of the perturbation energy is smaller than that for the case without control.For the case where the body force acts on both the separation bubbles,the secondary separation bubble is removed,the isoline stays in the central part of the channel,and thereby the viscous term has less effects on the amplification rate of which the peak value could be the maximum one for some control number.

Circular Scale of Time and Its Use in Calculating the Schrödinger Perturbation Energy of a Non-Degenerate Quantum State

The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schrödinger perturbation energy of a non-degenerate quantum state. This seems to be done in a more simple way than with the aid of any other of the perturbation approaches of a similar kind. As an example of the theory suitable to comparison is considered the Feynman diagrammatic method based on a straight-linear scale of time which represents a much more complicated formalism than the present one. All diagrams of the approach outlined in the paper can obtain as their counterparts the algebraic formulae which can be easily extended to an arbitrary Schrödinger perturbation order. The calculations and results descending from the perturbation orders N between N = 1 and N = 7 are reported in detail.

Circular Scale of Time as a Way of Calculating the Quantum-Mechanical Perturbation Energy Given by the Schrodinger Method

The Schrodinger perturbation energy for an arbitrary order N of the perturbation has been presented with the aid of a circular scale of time. The method is of a recurrent character and developed for a non-degenerate quantum state. It allows one to reduce the inflation of terms necessary to calculate known from the Feynman’s diagrammatical approach to a number below that applied in the original Schrodinger perturbation theory.

Hot Vertical-Displacement-Event Process due to Internal Energy Perturbations for HL-2M Tokamak Plasma

During the tokamak operation, variation of the stored energy can cause internal perturbations of the plasma. These perturbations may develop into large-scale vertical movement of the whole column for the vertically elon- gated tokamak, eventually generating the hot vertical displacement event （VIDE,）. It will cause considerable damage to the machine. In this work, the hot VDE process due to stored energy perturbations is investigated by a mature non-linear time-evolution code DINA. The influence on the vertical instability, the displacement direction and the electromagnetic loads on in-vessel components during the hot VDE are analyzed. It is shown that a larger perturbation leads to faster development of the vertical instability. Meanwhile the variation of the Shafranov shift, due to the energy change, is related to the VDE direction. The vertical electromagnetic force on the vacuum vessel and the halo current flowing in the divertor baffle become larger in the case of VDE moving towards the X point.

Circular Scale of Time and Construction of the Schrodinger Perturbation Series for Energy Made Simple

Physically the examined perturbation problem can be regarded as a set of collision events of a time-independent perturbation potential with a quantum system. As an effect of collisions there is an expected definite change of energy of an initially unperturbed state of the system to some stationary perturbed state. The collision process certainly occupies some intervals of time which, however, do not enter the formalism. A striking property is the result of a choice of the sequence of collisions according to the applied circular scale of time: the scale produces almost automatically the energy terms predicted by the Schrödinger perturbation theory which usually is attained in virtue of complicated mathematical transformations. Beyond of the time scale and its rules—strictly connected with the perturbation order N introduced by Schrödinger—a partition process of the number N-1 is applied. This process, combined with contractions of the time points on the scale, provides us precisely with the perturbation terms entering the Schrödinger theory.

Planck’s Oscillators at Low Temperatures and Haken’s Perturbation Approach to the Quantum Oscillators Reconsidered

In the first step the extremal values of the vibrational specific heat and entropy represented by the Planck oscillators at the low temperatures could be calculated. The positions of the extrema are defined by the dimensionless ratios between the quanta of the vibrational energy and products of the actual temperature multiplied by the Boltzmann constant. It became evident that position of a local maximum obtained for the Planck’s average energy of a vibration mode and position of a local maximum of entropy are the same. In the next step the Haken’s time-dependent perturbation approach to the pair of quantum non-degenerate Schr?dinger eigenstates of energy is re-examined. An averaging process done on the time variable leads to a very simple formula for the coefficients entering the perturbation terms.

GENERAL DECAY FOR A QUASILINEAR SYSTEM OF VISCOELASTIC EQUATIONS WITH NONLINEAR DAMPING

In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.

Free energy perturbation(FEP)-guided scaffold hopping

Scaffold hopping refers to computer-aided screening for active compounds with different structures against the same receptor to enrich privileged scaffolds,which is a topic of high interest in organic and medicinal chemistry.However,most approaches cannot efficiently predict the potency level of candidates after scaffold hopping.Herein,we identified potent PDE5 inhibitors with a novel scaffold via a free energy perturbation(FEP)-guided scaffold-hopping strategy,and FEP shows great advantages to precisely predict the theoretical binding potenciesΔGFEPbetween ligands and their target,which were more consistent with the experimental binding potenciesΔGEXP(the mean absolute deviations|ΔGFEP-ΔGEXP|<2 kcal/mol)than thoseΔGMM-PBSAorΔGMM-GBSApredicted by the MM-PBSA or MM-GBSA method.Lead L12 had an IC_(50) of 8.7 nmol/L and exhibited a different binding pattern in its crystal structure with PDE5 from the famous starting drug tadalafil.Our work provides the first report via the FEPguided scaffold hopping strategy for potent inhibitor discovery with a novel scaffold,implying that it will have a variety of future applications in rational molecular design and drug discovery.

Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam

Abstract In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t M X.

STABILIZATION OF EULER-BERNOULLI BEAM WITH A NONLINEAR LOCALLY DISTRIBUTED FEEDBACK CONTROL

This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t →∞.