Radius dependent shift of surface plasmon frequency in large metallic nanospheres: theory and experiment

Theoretical description of oscillations of electron liquid in large metallic nanospheres (with radius of few tens nm) is formulated within random-phase-approximation semiclassical scheme. Spectrum of plasmons is determined including both surface and volume type excitations. It is demonstrated that only surface plasmons of dipole type can be excited by homogeneous dynamical electric field. The Lorentz friction due to irradiation of electro-magnetic wave by plasmon oscillations is analyzed with respect to the sphere dimension. The resulting shift of resonance frequency turns out to be strongly sensitive to the sphere radius. The form of e-m response of the system of metallic nanospheres embedded in the dielectric medium is found. The theoretical predictions are verified by a measurement of extinction of light due to plasmon excitations in nanosphere colloidal water solutions, for Au and Ag metallic components with radius from 10 to 75 nm. Theoretical predictions and experiments clearly agree in the positions of surface plasmon resonances and in an emergence of the first volume plasmon resonance in the e-m response of the system for limiting big nanosphere radii, when dipole approximation is not exact

Determination of Inertia Forces Acting on Break Bulk Cargo en Route

The paper presents the analytical method of defining inertia forces that act on break bulk cargo as a result of the oscillatory motion of the vessel exposed to the effect of ambient forces. Considering that the linear models of roll, pitch and heave applicable in this case, the problem is solved by expressing the angle of heel, the angle of pitch, and the amplitude of heave. The obtained functions are differentiated and the inertia forces are determined by means of applying the Newton's second law