Stretching in a model of a turbulent flow

Using a multi-scaled, chaotic flow known as the KS model of turbulence [J.C.H. Fung, J.C.R. Hunt, A. Malik, R.J. Perkins, Kinematic simulation of homogeneous turbulence by unsteady random fourier modes, J. Fluid Mech. 236 (1992) 281-318], we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.     

Tunnelling process between a semiconductor or a metal and a polymer

The tunnelling lifetime of an electron lying in a p-type orbital localised at a given distance from a semiconductor or a metal is calculated by using Bardeen's method. It is then shown that even in the absence of broad bands, the hole injection process from semiconductors and metals into polymers should follow a Fowler-Nordheim dependence, provided that the current is not bulk-limited. In the semiconductor case, the current can be expressed by a fully analytical formula, and by an approximate one in the case of a metal. It is demonstrated that the effective Fowler-Nordheim barrier is not the mere difference between the metal work function or the semiconductor electron affinity and the HOMO level of the polymer, but a simple function of both levels. Received 6 April 2001 and Received in final form 29 May 2001     

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular ?-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.     

Dynamics of a two-level trapped ion in a cavity

In the present paper we consider the case of a two-level ion in a cavity in the presence of a single mode field linearly polarized. We suppose that the ion is free to move along the polarization direction and trapped by a harmonic potential along the other two directions. By multiple path integration we derive the density matrix of the system and we study its dynamics. We assume an initial electromagnetic vacuum. This initial condition for the present system, compared with any other initial photonic state, gives new and higher order leading terms with respect to an expansion in powers of the inverse of the volume. Further after such an expansion there appears a first order term that originates from the combined interaction of the two-level system (qubit) with the quantum motion of the ion and the electromagnetic field in the cavity. We notice that the dynamics of the present system is very rich and can be studied exhaustively in the present framework.     

Frequency noise suppression in a diode laser locked to a travelling wave resonator incorporating a Brewster prism

A polarisation locking technique was applied to stabilise an extended cavity diode laser using a travelling wave resonator incorporating a Brewster prism. Despite the fact that the employed unbalanced detection was sensitive to optical power fluctuations, the in-loop photodetector measured 90 dB of noise suppression at 10 Hz in comparison to the free running frequency noise spectrum. Excess intensity noise measured with an out-of-loop detector, indicated the presence of correction-correlated noise in the output of the stabilised diode laser.     

Spontaneous CP violation in a SUSY model with a complex CKM

It is pointed out that the recent measurement of the angle γ   of the unitarity triangle, providing irrefutable evidence for a complex Cabibbo–Kobayashi–Maskawa (CKM) matrix, presents a great challenge for supersymmetric models with spontaneous CP violation. We construct a new minimal extension of the minimal supersymmetric standard model (MSSM), with spontaneous CP breaking, which leads to a complex CKM matrix, thus conforming to present experimental data. This is achieved through the introduction of two singlet chiral superfields and a vector-like quark chiral superfield which mixes with the standard quarks. A Z₃$Z_3$ symmetry is introduced in order to have a potential solution to the strong CP problem.     

Capillary Interactions between a Probe Tip and a Nanoparticle

To understand capillary interactions between probe tips and nanoparticles under ambient conditions, a theoretical model of capillary forces between them is developed based on the geometric relations. It is found that the contribution of surface tension force to the total capillary force attains to similar order of magnitude as the capillary pressure force in many cases. It is also shown that the tip shape and the radial distance of the meniscus have great influence on the capillary force. The capillary force decreases with the increasing separation distances, and the variance of the contact angles may change the magnitudes of capillary forces several times at large radial distances. The applicability of the symmetric meniscus approximation is discussed.     

Ginzburg-Landau simulation for a vortex around a columnar defect in a superconducting film

By means of numerical simulations based on Ginzburg-Landau theory, we study the vortex depinning from a columnar defect in a superconducting film. We evaluate the limiting thickness of the film, below which the depinning does not occur even under an application of the magnetic field perpendicular to the columnar defect. The limiting thickness is a measure of the pinning strength of the columnar defect. The dependence of this limiting thickness on the magnitude of the applied field is obtained for two types of columnar defects.     

Generation of a Sub-10fs Laser Pulse by a Ring Oscillator with a High Repetition Rate

A compact femtosecond Ti：sapphire ring oscillator composed of chirped mirrors is designed. By accurately optimizing the intra-cavity dispersion and the mode locking range of the ring configuration, we generate laser pulses as short as 7.7fs with a repetition rate as high as 745 MHz. The spectrum spans from 660nm to 94Ohm and the average output power is 480mW under the cw pump laser of 7.5 W.     

Exact solutions for a diffusion equation with a nonlinear external force

This work is devoted to investigate the solutions of the one-dimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=−k(t)x+K/x+κx|x|^α−1η[ρ(x,t)] into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.     

Exact transmission state of a Bose-Einstein condensate in a near-harmonic trap

We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution.     

Gradient expansion for a spiral phase in a spin-fermion model

Starting from a doped spin-fermion model for high-temperature superconductors, we derive an effective continuum theory for the spin degrees of freedom by means of a gradient expansion around a spiral spin configuration. By integrating out the fermions in a path-integral representation, we obtain an effective spin-action. An incommensurate, planar spiral configuration for the spin-background is assumed. The long-wavelength limit is obtained by expanding the effective action in powers of a short distance cutoff. The occurring infinite series can be summed to all orders of the coupling constant by exploiting the constraint that the order parameter lives on a circleS ₁. It is shown that the low-energy limit of the effective action can be mapped onto a O(2) nonlinear model and an additional term due to parity breaking.     

STM tunneling through a quantum wire with a side-attached impurity

The STM tunneling through a quantum wire (QW) with a side-attached impurity (atom, island) is investigated using a tight-binding model and the non-equilibrium Keldysh Green function method. The impurity can be coupled to one or more QW atoms. The presence of the impurity strongly modifies the local density of states of the wire atoms, thus influences the STM tunneling through all the wire atoms. The transport properties of the impurity itself are also investigated mainly as a function of the wire length and the way it is coupled to the wire. It is shown that the properties of the impurity itself and the way it is coupled to the wire strongly influence the STM tunneling, the density of states and differential conductance.     

Phonon-Assisted Resonant Tunnelling through a Triple-Quantum-Dot： a Phonon-Signal Detector

We study the effect of electron-phonon interaction on current and zero-frequency shot noise in resonant tunnelling through a series triple-quantum-dot coupling to a local phonon mode by means of a nonperturbative mapping technique along with the Green function formulation. By fixing the energy difference between the first two quantum dots to be equal to phonon frequency and sweeping the level of the third quantum dot, we find a largely enhanced current spectrum due to phonon effect, and in particular we predict current peaks corresponding to phonon-absorption and phonon-emission assisted resonant tunnelling processes, which show that this system can be acted as a sensitive phonon-signal detector or as a cascade phonon generator.     

Scattering of a relativistic scalar particle by a cusp potential

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low-momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.     

Dynamics of a degenerate parametric oscillator in a squeezed reservoir

Dynamics of a cavity mode which, in addition to interacting to an outside field with squeezed fluctuations, is simultaneously submitted to linear and parametric amplification processes is discussed in the Markovian approximation. The master equation for a density matrix of the cavity field is solved analytically in the Heisenberg picture. Long time asymptotic properties of the cavity mode are studied in the whole range of the evolution parameters and the corresponding decoherence effects are reported. It is also shown that in an appropriate regime of the evolution parameters there exists a unique steady state such that all initial density matrices evolve towards it. This allows engineering cavity states with desired properties.     

Experimental Investigation on a Fibre-Optic Hydrophone with a Cylindrical Helmholtz Resonator

A novel mechanical anti-aliasing filtering fibre-optic hydrophone with a cylindrical Helmholtz resonator is con- structed and tested. The experimental results show that the hydrophone has a function of low-pass filtering. The low frequency acoustic sensitivity is about -160 dB （1 rad/#Pa）, and the response curve has a resonance deter- mined by the Helmholtz resonator. Theoretical and experimental results both show that the resonant frequency moves towards high frequency with the increasing orifice diameters. The sensitivity attenuation of high frequency is larger than lOdB. This new fibre-optic hydrophone is a prototype device for a class of sensors used to eliminate the aliasing in future sonar systems.     

Analogies between a Meniscus and a Cantilever

Systematic and quantitative analyses of exact analogies between a meniscus and an elastica are performed. It is shown that the two governing equations take the same style after coordinate translation and scale transformation. The morphologies of the liquid bridge and the cantilever are calculated in terms of elliptic integrations, which can be reduced to the same shape,after converting the boundary conditions. The present analyses can make us grasp the nature of this physical phenomenon deeply and show some inspiration for designing the analogy experiments. Moreover, the calculated results are helpful to engineering applications, such as design and fabrication of MEMS, and micro-manipulations in micro/nano- technology.     

Tracking a single fluorescent molecule with a confocal microscope

We consider the problem of tracking a single fluorescent molecule in both two and three dimensions using a confocal laser scanning microscope. An estimate of the position of the molecule is generated from the measured fluorescence signal through the use of parameter estimation theory. This estimate is used in a nonlinear controller designed both to track the position of the molecule and to provide good measurements for use in the estimation algorithm. The performance of the approach is investigated through numerical simulation for molecules undergoing diffusion and directed transport and the capabilities of the controller relative to experimental limitations are discussed.     

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.