Negative nonconservative forces: optical "tractor beams" for arbitrary objects

Based on the conservation of linear momentum on scattering from arbitrary objects, we demonstrate the generation of nonconservative optical forces that act in a direction opposite to the propagation of the incident beam. The concept can be applied to tailor the force fields produced on nonabsorbing bodies regardless of their sizes and shapes.     

Single gradientless light beam drags particles as tractor beams

Usually a light beam pushes a particle when the photons act upon it. We investigate the optical forces by nonparaxial gradientless beams and find that the forces can drag suitable particles all the way towards the light source. The major criterion of realizing the backward dragging force is the strong nonparaxiality of the light beam, which contributes to the pulling force owing to momentum conservation. The nonparaxiality of the Bessel beam can be manipulated to possess a dragging force along both the radial longitudinal directions, i.e., a "tractor beam" with stable trajectories is achieved.     

On the concept of attractor

This note proposes a definition for the concept of attractor, based on the probable asymptotic behavior of orbits. The definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.     

On the way towards crystallized beams: the transverse temperature of particle beams

The cooling of particles in storage rings depends on the coupling between the longitudinal and transverse “temperatures” of the stored beam. This coupling is studied in the limit of relatively sparse beams, and is found to depend sensitively on the relative strengths of the focusing forces in the two transverse dimensions, which determine the ratio of the periods of the betatron oscillations.     

On the concept of spectral singularities

In this paper, we discuss the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.     

On the radiation coherence limits of electron beams

Radiation coherence limits of electron beams, caused by uncertainty of phases of individual emitters, systematic variations of the beam current density profile, and an increase in the beam density are estimated.     

On the two frequency spectra of Timoshenko beams

This paper is concerned with the question of whether there are, indeed, two distinct spectra of frequencies for the transverse vibrations of Timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and, more recently, for beams supported in an arbitrary manner. Elementary analysis leads to the conclusion that there is only a single frequency spectrum; in the particular case of the simply supported beam the “two frequency spectra” viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex, dynamical behavior of Timoshenko beams.     

On the foundations of the physical probability concept

An exact formulation of the frequency interpretation of probability is proposed on the basis of G. Ludwig's concept of physical theories. Starting from a short outline of this concept, a formal definition of weak approximate reduction is developed, which covers the reduction of probability to frequency as a special case.     

基尔霍夫定律中的“独立回路”

对电路理论基尔霍夫定律中“独立回路”概念进行讨论,提出较为合理的独立回路的概念,并运用线性代数、几何方法、拓扑图论等方法,分别对平面电路网络和立体电路网络进行讨论,证明在此规定下基尔霍夫方程的独立性和解的确定性.     

On the damped vibratory response of curved viscoelastic beams

An analysis is given of the damped forced vibratory response of viscoelastic beams with small initial curvature in order to explore the interaction of initial curvature with both extensional and shear deformation, as they provide energy dissipation mechanisms for the damped response. A non-dimensional variational statement is developed which governs the problem of the forced vibratory response of slightly curved Timoshenko beams including in-plane deformation, and appropriate parameters are defined. In particular, initial rise and shear parameters are seen to play important roles in the results.Numerical results are presented for the first three modes for both simple and clamped support conditions. In general, even a slight amount of initial curvature has a significant effect in decreasing the damped response for the first mode, and the actual effect is influenced strongly by the shear parameter. Initial curvature has a smaller influence on the higher modes. An understanding of when extensional or shear energy dissipation is dominant for certain ranges of values of the curvature and shear parameters is obtained by actual plots involving the appropriate form of energy dissipation. In general, extensional energy dissipation tends to dominate in the first mode for both support conditions, although the clamped beam tends to favor shear dissipation over a certain range of parameter values. The dominance of the shear mechanism, however, increases markedly for the higher modes for both support conditions.