The interaction between a disclination in a nematic liquid crystal and a rubbed surface

For the case of a rubbed surface with a finite anisotropic surface tension, a model is developed for the structure and energy of a surface disclination and of an edge disclination near the surface. It is found that there is an energy barrier against detaching a disclination from the surface, and also that there is a critical distance within which a disclination is attracted, and beyond which it is repelled, by the surface. These properties may provide a measurement of the anisotropy of the surface tension.     

Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

Design of a Reflective Aspherical Surface of a Compact Beam-Shaping Device

A compact beam-shaping device with a reflective aspherical surface is proposed. The device converts a circular symmetric Gaussian beam from a laser into a uniform distribution on a target plane. The device consists of a laser, a reflective aspherical surface formed on the base plane inclined by 45° against the optical axis, and a spacer. The surface is designed for an optical device used as a transmitter of indoor wireless optical communication, which is one of the promising applications. The designed surface is obtained by approximation using polynomial. Beam shaping of a simulated surface and a uniform intensity distribution on the target plane is obtained. The intensity distribution generated by the surface is numerically simulated and evaluated if the surface is misaligned. It is clarified that the generated distribution is tolerable for the misalignment.     

Enhancement of an Instability by Internal Feedbacks in a Plasma

The electron-ion instability is excited in counterstreaming ion beams and plasma system. The instability is a new type of standing oscillations whose wavelength is given by D/n, where D is the distance between boundaries and n is an integer. The amplitude is controlled by a difference between the velocities of the beams, which changes the phase of a feedback loop. The internal feedback is caused by a reflected wave and by a coupling between the boundaries. Temporal evolution of the instability is measured and is found to agree with numerical solutions of the Van der Pol equation including a feedback term. A measured growth rate is proportional to the square of the oscillation amplitude.     

Bose-Einstein condensation and the glassy state

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.     

Distribution corresponding to classical thermodynamics

A distribution corresponding to classical thermodynamics is constructed. The concept of degrees of freedom is generalized and a concept of temperature-dependent number of collective degrees of freedom is introduced. A relationship between the theory of numbers and mesoscopic physics is established. A geometric interpretation of spinodal as a curve of maximum entropy and as a catastrophe in a quasi-static Caratheodory process is given. A concept of local ideal gas is introduced. The phase transition of fluids to a dispersed system is determined. The distribution obtained is numerically compared with the distribution for a van der Waals gas in the Hougen-Watson diagram.     

Reproduction of a protocell by replication of a minority molecule in a catalytic reaction network

For understanding the origin of life, it is essential to explain the development of a compartmentalized structure, which undergoes growth and division, from a set of chemical reactions. In this study, a hypercycle with two chemicals that mutually catalyze each other is considered in order to show that the reproduction of a protocell with a growth-division process naturally occurs when the replication speed of one chemical is considerably slower than that of the other chemical, and molecules are crowded as a result of replication. It is observed that the protocell divides after a minority molecule is replicated at a slow synthesis rate, and thus, a synchrony between the reproduction of a cell and molecule replication is achieved. The robustness of such protocells against the invasion of parasitic molecules is also demonstrated.     

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

In the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction.     

弯曲光纤针尖及其法向力压电探测技术

本文介绍一种弯曲光纤针尖及其法向力压电探测的新技术.与目前普遍采用的方法不同,弯曲针尖的制作是先利用电阻丝加热,将光纤弯曲成所需的角度,然后再在缓冲氢氟酸中腐蚀成针尖,得到曲率半径为300μm,弯曲角度为120°,长度为500μm的弯曲针尖.同激光或电弧熔拉、弯曲的方法相比,这种方法工艺简单,成本低廉.由弯曲针尖与蜂鸣器压电片组成的悬臂,利用压电片的正、逆压电效应实现弯曲针尖法向力的非光学法探测.实验表明,这种弯尖法向力的探测较直尖切变力具有更高灵敏度,探测距离提高了一倍以上,给实际应用带来很大的便利.     

Detailed field model for DH stripe lasers

The field problem for DH stripe lasers is solved, using a two-dimensional model; the field variation perpendicular to the junction plane is found from a slab model, whereas the transverse variation is calculated using a method applicable to any complex permittivity profile. The origin of transverse variations in the permittivity is described by including current spreading, temperature variations and the carrier profile. The permittivity is used directly and not fitted by a parabola or a step. The fact that a large fraction of the intensity may be propagating in then-andp-layers, is taken into account by introduction of an effective permittivity. The model is applied to a practical example, and the threshold current is found as a function of active-layer thickness and stripe width. It is described how the model can be used both below and above the threshold.     

Completely mixed state is a critical point for three-qubit entanglement

Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement.     

Poisson brackets and the Feynman problem

A derivation of a pair of Maxwell equations which is based on the concept of a Poisson structure on a manifold is given. The idea is geometric in character, and is extended to a generalized algebra. The special case of the dynamics for a particle in a Yang-Mills field is obtained as a consequence of the generalized case.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Gain calculation of a free-electron laser operating with a non-uniform ion-channel guide

Amplification of an electromagnetic wave by a free electron laser (FEL) with a helical wiggler and an ion channel with a periodically varying ion density is examined. The relativistic equation of motion for a single electron in the combined wiggler and the periodic ion-channel fields is solved and the classes of possible trajectories in this configuration are discussed. The gain equation for the FEL in the low-gain-per-pass limit is obtained by adding the effect of the periodic ion channel. Numerical calculation is employed to analyse the gain induced by the effects of the non-uniform ion density. The variation of gain with ion-channel density is demonstrated. It is shown that there is a gain enhancement for group I orbits in the presence of a non-uniform ion-channel but not in a uniform one. It is also shown that periodic ion-channel guiding is used to reach the maximum peak gain in a low ion-channel frequency (low ion density).     

Multiple-reflection effects in hadron-nucleus scattering: (I). Cluster expansion of the optical potential

A basic assumption underlying the high-energy hadron-nucleus optical potential is that no target nucleon is struck more than once. Although this condition is satisfied at high energy, such is not the case in the vicinity of medium-energy resonances, where the amplitude for the projectile to undergo multiple reflections between two target nucleons is quite large. As a remedy for this problem, the multiple-scattering series is rearranged such that the optical potential can be expressed as a cluster expansion. The lowest order optical potential is modified by a two-body cluster term, which is a sum of all possible reflections of the projectile between a pair of target nucleons. This term is evaluated for a model potential within the formalism of Foldy and Walecka: it is substantially smaller than the contribution of a single reflection, and its overall effect is small under certain additional restrictions. If the independent-pair picture of nuclei is valid, then the three-body cluster term may be small, and the lowest order Glauber optical potential can provide a self-consistent picture of hadron-nucleus interactions, even though a term-by-term expansion of the multiple-scattering series does not provide such assurance.     

Transmission of structure-borne sound from a beam into an infinite plate

An analytical study of transmission of structure-borne sound from a semi-infinite beam into an infinite, isotropic plate is presented. The beam is assumed to carry a torsional, a quasi-longitudinal and bending wave and the transmission is obtained with the help of the admittances of the beam and the plate. The analysis is restricted to the case of low frequencies but is otherwise general; thus due regard is given not only to the bending wave of the plate but also to the other propagating waves and to the local reactions. An interesting result from the study is that a bending wave on the beam will transfer a substantial part of its power into quasi-longitudinal and transverse waves in the plate, especially if the plate is thin compared with the beam. This is thought to be a factor that is important and not so easily quantifiable in the analysis of a complex structure. The local reactions on the other hand are of small importance for the power transmission from a torsional and quasi-longitudinal wave on the beam but may be important for the transmission of a bending wave, especially if the Young's modulus of the beam is larger than that of the plate.     

The magnetic susceptibilities of NO and OH

A non-isothermal kinetic equation for the distribution function of a sub-system weakly coupled to a bath is derived by modification of the analysis and assumptions of a previous paper [1]. The equation has the form of a generalized non-isothermal Fokker-Planck equation when it is linearized in thermodynamic gradients and only terms through second order in the coupling parameters are retained. Higher order terms in the coupling parameter do not diverge with time. The equation is compared with certain ‘exact’ model results of Ullersma and with the coherence time method. The equation is used to calculate a jump rate for diffusion of a harmonic particle weakly coupled to a lattice and it is found that the jump rate becomes independent of the mass of the particle for a heavy enough particle. The source of the discrepancy of this result with a similar calculation of Prigogine and Bak is indicated. The model of the jump rate is inappropriate for diffusion in a thermal gradient and more appropriate models of the jump are briefly considered. A brief comparison of the derivation of the kinetic equation with the Fano coherence time approximation is made and a difference is noted.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.     

Wave-front reversal of multifrequency continuous emission by Bragg scattering from phase regular inhomogeneities

The possibility of wave-front reversal of continuous multifrequency emission with a wide line spectrum (in particular, emission of lasers operating on cascade vibrational-rotational transitions of diatomic molecules, e.g., HF or CO) is analyzed; the reversal is based on Bragg scattering from a spatial phase hologram that is recorded in a resonance-absorbing medium by emission with a frequency different from any of the reversed-signal frequencies. The mechanism of formation of a spatial phase hologram and the features of optical Bragg scattering on such structures are analyzed. It is shown that a scattered wave-front is complex conjugate to one of the waves recording the phase grating. An optical system for wave-front reversal is proposed and the Bragg scattering efficiency is estimated for a particular example. The analysis indicates that the proposed system does not exhibit frequency selectivity and is basically suitable for wave-front reversal of emission with a broad line spectrum. The main problem is to choose a medium with resonance absorption at the center of a multifrequency emission spectrum and with complete transparency for the reversed signal.