Effective boundary field theory for a Josephson junction chain with a weak link

We show that a finite Josephson junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.     

A general model of the axle vibration in piezoelectric motors

In the present work a general model of the vibrational behavior of the axle of a piezoelectric motor is proposed. In this motor, a cylinder-shaped permanent magnet, which act as a rotor, is pressed in contact with an end of a steel axle by means of the magnetic forces. The other end of the axle is fitted at the center of a rotating traveling wave generator. A piezoelectric membrane, vibrating in a flexural anti-symmetrical mode, or a thick disk, vibrating in a radial anti-symmetrical mode, can be exploited as traveling wave generators. In the first case a bending moment, in the second case a transverse force is applied to the axle. In both cases, if the driving frequency coincides with a resonance frequency of the axle, the axle acts as a resonant displacement amplifier; a continuous slipping takes place between the axle and the rotor, and a torque is transmitted to the rotor. The proposed model is able to describe the axle vibrational behavior when it is excited by a bending moment, by a transverse force, and also when these two excitations are simultaneously applied. The axle is modeled as a four-port system and all its transfer functions, as well as the transversal displacement along the axle at each frequency can be easily computed. Computed results have been compared with experimental measurements carried out on two motor prototypes that exploit as traveling wave generators a membrane and a disk, respectively. A good agreement was obtained by properly taking into account the loading effect of the generator on the axle.     

Universal behavior of the energy of trapped few-boson systems with large scattering length

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length a(osc). The atoms are assumed to interact through a short-range potential with a scattering length a, and the short-distance behavior of the three-body wave function is characterized by a parameter theta. For large positive a/a(osc), the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of a and theta. For other states, the theta dependence of the energy is strong, but the energy is independent of a for |a/a(osc)|>1.     

Reorientation of a nonspherical capsule in creeping shear flow

The dynamics of a capsule and a biological cell is of great interest in chemical engineering and bioengineering. Although the dynamics of a rigid spheroid is well understood by Jeffery's theory, that of a spheroidal capsule remains unclear. In this Letter, the motion of a spheroidal capsule or a red blood cell in creeping shear flow is investigated. The results show that the orientation of a nonspherical capsule is variant under time reversal, though that of a rigid spheroid is invariant. Surprisingly, the alignment of a nonspherical capsule over a long time duration shows a transition depending on the shear rate, which can be utilized for a particle-alignment technique. These findings form a fundamental basis of the suspension mechanics of capsules and biological cells.     

Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<-1, however, the potential has long range, with a(ad)>0 and b(ad)>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.     

Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation

The normalized relaxation modulus represents a salient feature of viscoelastic materials and its determination is of great significance for various applications. From the normalized relaxation modulus, for instance, one can derive the loss factor of a viscoelastic polymer and judge whether a material is suitable for damping applications or not. By using dimensional analysis and the elastic–viscoelastic correspondence principle, the normalized relaxation function of a linear viscoelastic material obtained from indentation relaxation tests is shown to depend only on the indentation load but not on the indenter geometry and the shape of the indented solid. The result could enable circumvention of the difficulties encountered in the calibration of the indenter geometry and the preparation of indented samples. Numerical simulations are performed on a number of cases of practical interest, including the spherical indentation test of a soft layer lying on a rigid substrate, a flat punch indenter indenting into a soft layer with a rough surface bonded to a rigid substrate, a rigid indenter with irregular shape indenting into a particle, inclined contact of a cylindrical indenter with a cylinder, and indentation of porous substrates. The numerical examples demonstrate that the conclusion from the theoretical analysis is valid for all these situations.     

Method for computing the intensity distribution in the image plane of an aberration-free lens with allowance for the wave properties of light

For the Gaussian model of a lens, a Green-function-based method is proposed to compute the intensity distribution in the lens image plane. The method is used to accomplish several test tasks, which include the simulation of the image of a square area, the diffraction by an infinitely long slit, the focusing of a convergent wave with a Gaussian amplitude profile in the focal waist region, and the image of a surface representing an analog of a diffraction grating. After a suitable modification, the method can serve for simulating the propagation of light waves within a real lens and for solving other applied problems.     

Physical adsorption and surface plasmons

The quantum mechanical formulation of the screening of a point charge by surface plasmons is extended to describe the coupling of a fluctuating atomic dipole with a metallic surface of planar, spherical or cylindrical shape. This allows for the calculation of the nonretarded Van der Waals attraction of an atom by a solid surface in the three different geometries. Applications of the theoretical formulae are made to obtain numerical values of the dispersion energy by a spherical particle, a spherical pore, a thin film, a slot-like prore, a cylindrical fiber or a cylindrical pore.     

The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time.     

Reconstruction of the acoustic impedance profile in a plate using an inverse spectral procedure

An inverse spectral procedure was applied to reconstruct the acoustic impedance profile along the thickness direction of a plate using its thickness resonance frequencies, density and thickness. For a successful reconstruction, the material-property profile must be symmetric about the mid-plane of the plate. Several cases of numerical simulations, including plates with a few layers and with a high number of layers are described. The calculated resonance frequencies were used to reconstruct the acoustic impedance profile, a process that was successful for all cases. We assume that a plate with a high number of layers, each with a different but constant acoustic impedance, simulates a plate with a smoothly varying acoustic impedance profile. It can be concluded that such a plate, which generates small, virtually undetectable, internally reflected waves, can also be reconstructed. In the special case of a plate of unknown thickness and unknown but constant density, the method is still useful, because a relative variation of the material property can be reconstructed using only the resonance frequencies. An experiment using a resonance-mode electromagnetic acoustic transducer (resonance-mode EMAT) is also described. EMAT is a non-contact ultrasonic method that can measure thickness resonance frequencies, making it appropriate for this method. Some examples of applications are measurement of the temperature profile inside a rolled metal sheet, measurement of a clad metal plate, and monitoring of a metal casting.     

Quantum speed limit for mixed states in a unitary system

Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it, we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit (QSL) of a mixed state. We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system, which automatically reduces to the quantum speed limit induced by the Fubini-Study metric for pure states. The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state, where we have to make a singular value decomposition (SVD) on the inner product between the two eigenvector matrices of the initial and target states. By combing these results, a lower bound for the evolution time of a general mixed state is presented. In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references, two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically, respectively. All conclusions derived in this work are independent of the eigenvalues of the mixed state, which is in accord with the evolution properties of a quantum unitary system.     

How Pressure Became a Scalar,Not a Vector

The gradual emergence of a science of hydrostatics during the course of the seventeenth century is testament to the fact that a technical concept of pressure that was up to the task was far from obvious. The first published version of a theory of hydrostatics containing the essentials of the modern theory appeared in book 2 of Isaac Newton’s Principia. Newton derived the propositions of hydrostatics from a definition of a fluid as a medium unable to withstand a distorting force. Newton’s reasoning required that pressure be understood as a force per unit area acting on either side of imaginary planes within the body of a fluid. For a fluid in equilibrium, the forces at some location within a fluid are independent of the orientation of such planes. As Newton came to realize, within the body of a liquid, pressure acts equally in all directions so that there is no resultant pressing in any direction. Pressure has an intensity but not a direction. In modern terms, it is a scalar, not a vector. Although earlier scholars such as Simon Stevin, Blaise Pascal, and Robert Boyle helped set the scene for Newton’s innovations, they were unable to transcend the common sense of pressure as a directed force acting on the solid surfaces bounding a fluid.     

Superradiant transition and its classical analogue

The two-level quantum model proposed by Preparata, according to which the interaction of a material system with a electromagnetic field can cause the loss of stability of the lower level, is examined. As a result of this instability, the role of the ground state is played by a periodic process generating superradiance (in contrast to laser radiation induced by overpopulation of the upper level). A classical analogue of a super-radiant quantum transition, a system of van der Pol-Duffing oscillators (generators) weakly coupled via a linear oscillator, is for the first time described. Such an analogue is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. It is shown that a necessary condition for the transition to intense energy exchange in the classical system is the instability of one of the nonlinear normal modes, similar to how the condition for a superradiant transition to occur is the instability of the ground state of a two-level quantum system coupled with a resonant electromagnetic field.     

Glassy-like states of bulk rare gases

Defining a glassy-like state of a system of bound atoms as a frozen, amorphous, thermodynamically unstable state, we consider a glassy-like state of a condensed rare gas as a configurationally excited state of bound atoms that tends to the thermodynamic equilibrium by diffusion of voids. The criterion for a critical cooling rate is the minimum cooling rate of the liquid state that leads to formation of a glassy-like state. Comparing this glassy-like state with that experimentally obtained by deposition of argon atoms on a cold target, we conclude that glassy-like states are characterized by short-range parameters. On the basis of cluster studies, peculiarities of the liquid aggregate states and glassy-like states are formulated. A glassy-like state of a cluster or a bulk system of bound atoms is a configurationally excited state below the freezing point; the liquid aggregate state exhibits configurational excitations but is characterized by thermal motion of atoms, consistent with the Lindemann criterion.     

具有态守恒赝隙的光子晶体中两能级原子自发辐射的增强与抑制

论证了在赝带隙光子晶体中存在一个全频率域态总数守恒规则，在完全带隙光子晶体中还存在一个局域态总数守恒规则.态总数守恒规则指出，如果一个光子晶体的态密度在某些频率范围存在相对于等效介质态密度的谷，则一定由其他频率范围内相对于等效介质态密度的峰来补偿.使用符合态总数守恒规则的态密度模型，解释了态密度调制导致的自发辐射谱增强、抑制、变窄、红移、蓝移以及谱分裂等光子晶体中的量子光学现象.该理论比较适合研究在具有赝带隙的光子晶体中大量随机分布的发光原子或分子的自发辐射行为. 关键词： 光子晶体 自发辐射 态密度 光子赝带隙     

Generation of a uniform high-density microwave plasma for CO2 lasers using orthogonal electric fields

To realize a CO₂ laser using a fast-axial-flow high-output-power microwave discharge excitation, we devised a technology for making the microwave discharge uniform by varying the oscillation direction of an electric field with time. We also verified the effectiveness of this technology. As a result, we succeeded in increasing the discharge uniformity to 70% of the laser-tube cross-sectional area and realized a high laser output power and a high laser efficiency. In the case of a microwave input power of 1450 W, a maximum laser output power of 273 W and a laser efficiency of 18.8% were achieved; in the case of a microwave input power of 1070 W, a laser output power of 214 W and a laser efficiency of 20.0% were achieved. At the time of maximum output power, a high input power density of 280 W/cm³, which is approximately 20 times that in a dc discharge method, was achieved. Thus, a high-output-power microwave-discharge-excited CO₂ laser has become feasible. PACS 42.60.By; 52.80.Pi     

Continuous monitoring of dynamical systems and master equations

We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes, only one of them interacting with external degrees of freedom, represented, in the first case, by a finite number of harmonic oscillators, and, in the second, by a sequence of atoms where each one interacts with a single mode during a limited time. Two distinct regimes appear, one of them corresponding to a Zeno-like behavior in the limit of large dissipation.     

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor.