Dynamical behaviour of multi-particle large-scale systems

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.     

Theoretical analysis of discrete contact problems with Coulomb friction

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable is analysed. It is shown that a solution exists for any F and is globally unique if F is sufficiently small. The Lipschitz continuity of this unique solution as a function of F as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary F > 0 is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient F is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector f. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives are given. Finally, the general approach is illustrated on an elementary example, whose solutions are calculated exactly.     

Diffusion of biostimulators into plant tissues

Biostimulators are substances able to enhance the immune system of cultivated crops and support plant metabolism. Their utilization helps to reduce the amount of chemicals used in agriculture. To perform the desired effect, a biostimulator must be able to penetrate into the plant tissue. The time of penetration however, is limited, since the biostimulator must remain in a liquid state. This is of great importance—especially in field conditions, where the treated plants are exposed to different weather condition and other extrinsic factors. A mathematical model based on diffusion mechanisms has been elaborated to describe the biostimulator transport process from penetration of the leaves into the plant’s inner tissues. By means of the effective diffusion coefficient of the prepared specific protein hydrolyzate, this model can be used to estimate the time necessary for the uptake of the minimal active amount of the biostimulator.     

Spectral manifestation of collective plasma oscillations quasi-resonant to eigenfrequencies of individual nanoparticles in a silver Island film

A doublet is revealed in the light extinction spectrum of a thin silver island film and the explanation of its nature is proposed. Based on the electron microscopy data, it is found that the doublet cannot be formed only by intrinsic resonances of individual islands. Because of interisland interactions, light can excite collective fields localized near the film. Resonant frequencies of these localized modes depend on the size, concentration, and arrangement of individual islands, whose plasma oscillation frequencies differ only slightly from one another.     

Off-resonance frequency filtered magnetic resonance imaging

One of the main problems with rapid magnetic resonance imaging (MRI) techniques is the artifacts that result from off-resonance effects. The proposed off-resonance frequency filtered MRI (OFF-MRI) method focuses on the elimination of off-resonance components from the image of the observed object. To maintain imaging speed and simultaneously achieve good frequency selectivity, MRI is divided into two steps: signal acquisition and post-processing.     

Atom lithography without laser cooling

Using direct-write atom lithography, Fe nanolines are deposited with a pitch of 186 nm, a full width at half maximum (FWHM) of 50 nm, and a height of up to 6 nm. These values are achieved by relying on geometrical collimation of the atomic beam, thus without using laser collimation techniques. This opens the way for applying direct-write atom lithography to a wide variety of elements.     

Infrared emissions, visible up-conversion, thermoluminescence and defect centres in Er3Al5O12 phosphor obtained by solution combustion reaction

The Er₃Al₅O₁₂ phosphor powders were prepared using the solution combustion method. Formation and homogeneity of the Er₃Al₅O₁₂ phosphor powders have been verified by X-ray diffraction and energy-dispersive X-ray analysis respectively. The frequency up-conversion from Er₃Al₅O₁₂ phosphor powder corresponding to the ²H_9/2 → ⁴I_15/2, ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, ⁴F_9/2 → ⁴I_15/2 and the infrared emission (IR) due to the ⁴I_13/2 → ⁴I_15/2 transitions lying at ∼410, ∼524, ∼556, 645–680 nm and at ∼1.53 μm respectively upon excitation with a Ti-Sapphire pulsed/CW laser have been reported. The mechanism responsible for the frequency up-conversion and IR emission is discussed in detail. Defect centres induced by radiation were studied using the techniques of thermoluminescence and electron spin resonance. A single glow peak at 430°C is observed and the thermoluminescence results show the presence of a defect center which decays at high temperature. Electron spin resonance studies indicate a center characterized by a g-factor equal to 2.0056 and it is observed that this center is not related to the thermoluminescence peak. A negligibly small concentration of cation and anion vacancies appears to be present in the phosphor in accordance with the earlier theoretical predictions.     

An ultra-stable referenced interrogation system in the deep ultraviolet for a mercury optical lattice clock

We have developed an ultra-stable source in the deep ultraviolet, suitable to fulfil the interrogation requirements of a future fully-operational lattice clock based on neutral mercury. At the core of the system is a Fabry–Pérot cavity which is highly impervious to temperature and vibrational perturbations. The mirror substrate is made of fused silica in order to exploit the comparatively low thermal noise limits associated with this material. By stabilizing the frequency of a 1062.6 nm Yb-doped fiber laser to the cavity, and including an additional link to LNE-SYRTE’s fountain primary frequency standards via an optical frequency comb, we produce a signal which is both stable at the 10^?15 level in fractional terms and referenced to primary frequency standards. The signal is subsequently amplified and frequency-doubled twice to produce several milliwatts of interrogation signal at 265.6 nm in the deep ultraviolet.     

Elementary-field modeling of surface-plasmon excitation with partially coherent light

We present a mathematical model and its numerical implementation for the analysis of the interaction of spatially partially coherent electromagnetic fields with micro- and nanostructured objects. The model is based on the decomposition of the incident field into a set of fully coherent but mutually uncorrelated elementary field modes, and the use of the Fourier Modal Method (FMM) with the S-matrix propagation algorithm. We apply the model to studies of the excitation of surface plasmons in thin metallic slabs, nanowires, and resonant structures. We demonstrate, e.g., that the plasmon excitation efficiency is not essentially affected by the degree of spatial coherence. However, certain plasmon interference effects can be efficiently smoothed out by using illumination with reduced coherence.     

Near-field imaging of point dipole with silver superlens

Making use of exact and quasistatic expressions for the field in near-field imaging of a point dipole by a thin silver slab, we calculate the point-spread function and the associated image resolution. We show that the resolution, which depends on the silver slab thickness and the dipole orientation, generally is better than the conventional diffraction limit and can be as high as λ/8. The results substantially agree with recent theoretical and experimental studies on 2D objects.