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.     

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.     

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.     

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.     

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.     

Displacement measurement technique for beam kinematics

It is proposed to develop a digital image correlation procedure that is suitable for beams whose kinematics is described by an Euler–Bernoulli hypothesis. As a direct output, the degrees of freedom corresponding to flexural and axial loads are directly measured. The performance of the correlation algorithm is evaluated by using a picture of a cantilever beam experiment. One load level is analyzed with the present algorithm. The latter is validated by comparing the displacement field with that given by a finite element based correlation algorithm. It is also shown that a locally buckled zone is detectable with the present procedure.     

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.     

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.     

Integrability of Characteristic Hamiltonian Systems on Simple Lie Groups with Standard Poisson Lie Structure

Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function on the group which is invariant with respect to conjugations. It is shown in this paper that such a system is always integrable.     

On the fluctuation enhanced conductivity of a superconductor: The correct evaluation of the Maki graph

According to Maki, a particular diagram—the Maki graph—gives a contribution to the fluctuation enhanced conductivity of a superconductor which is infinite in the case of a thin film. It is shown that this result is spurious and that it is due to a breakdown of the standard Green function impurity technique. A new method is developed which is strictly based on the Boltzmann equation. It is shown that the temperature dependent contribution of the Maki graph to the conductivity is negligibly small in a dirty metal.     

Periodic structure of acicular magnetic clusters in a magnetic liquid

The behavior of magnetic clusters in a magnetic liquid placed in a circular capillary is considered. When a uniform magnetic field is applied to the system, acicular clusters grow from the sediment, being aligned with the field. The interaction of the clusters as magnetic dipoles with one another and with an external gradient magnetic field is considered theoretically. In a nonuniform symmetric magnetic field with a peak, the cluster distribution is uniform near the peak. Such a distribution is fairly stable when the magnetic field gradient is varied over certain limits. The ordered (periodic) cluster configuration is realized experimentally, and it is shown that its period can be controlled. As the magnetic field gradient exceeds a certain threshold, the clusters are redistributed, forming a multirow hexagonal array.     

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).     

Mean curvature flow of a hyperbolic surface

A four-parameter family of self-similar solutions is obtained to the mean curvature flow equation for a surface. This family is shown to be stable with respect to a small deformation of a hyperbolic surface. At time instant t*, a singular point is formed within a finite time interval, that is accompanied by a change in the topology of the surface. The solution is continued beyond the singular point. A relationship between the parameters describing the hyperbolic surface before and after the change in the surface topology is obtained. A particular case is analyzed when the unperturbed surface is a cylinder. A cylindrical surface is weakly unstable with respect to a perturbation in the form of a “wide neck.” At the final stage of the development of the neck when its transverse size becomes much less than the cylinder radius at large distances from the neck, the surface flow in a wide region in the neighborhood of the neck is described by a universal two-parameter family of self-similar solutions. These solutions are stable with respect to small perturbations of the surface.     

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.     

Focusing of an X-ray spherical wave by a uniaxially bent crystal: Johann scheme and logarithmic spiral

Focusing of a spherical wave in the well-known Johann scheme is considered theoretically. An analytical formula for the size of the crystal bent surface reflecting radiation in the Johann scheme is derived. The intensity distribution near the focus is found. The spherical aberration of the diffracted beam is analyzed. Back scattering is shown to minimize the aberration. Spectral characteristics of an Johann spectrometer are discussed. The focusing of a spherical wave by a crystal bent into a logarithmic spiral is considered. It is shown that the Johann scheme is a specific case of a logarithmic spiral.     

Variational principles for scattering in the generator coordinate method

The generator coordinate method (GCM) wave function is used as a trial function in a Kohn type variational principle for scattering phase shifts. It is shown that a GCM trial function is a solution of the variational equations if the Hill-Wheeler integral equation is satisfied subject to an appropriate boundary condition. A new method for introducing the scattering boundary condition is presented. There is a uniqueness theorem for the phase shift.     

Heat transfer in locally heated liquid films moving under the action of gravity and gas flow

Heat transfer in a viscous liquid film moving under the action of gravity and a gas flow on a substrate with a locally heated rectangular area is investigated. The heat exchange coefficient is given on the liquid-gas surface; the heat flux to the liquid is given on the heated area; the substrate surface outside the heated area is heat-insulated. An analytical solution in a form of a convergent series is obtained for the liquid temperature distribution in the film. The influence of the dimensionless criteria on the obtained solution is analyzed. The effect of heat flux inhomogeneity on the temperature distribution is considered.     

同调谐振子谱空间上的对称性和参量双粒子模型

研究了同调谐振子谱空间上的对称性，通过适当的参量代换给出形象的图示. 得到归一化的本征函数解析表达式， 并证明了线性谐振子是同调谐振子的退化. 揭示出同调谐振子是参量双粒子模型，并给出该模型的相干态，该相干态自动包含用Glauber相干态构 造的奇、偶相干态. 关键词： 同调谐振子 赝角动量方法 本征值谱 本征函数 参量双 光子模型     

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.