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A general concept of perfect nonradiating modes in dielectric nanoparticles of an arbitrary shape is put forward. It is proved that such modes exist in axisymmetric dielectric nanoparticles and have unlimited radiative Q-factors. With smart…
Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The governing equation is the 3-d generalized Helmholtz equation…
Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems…
We study resonant response of an underdamped nanomechanical resonator with fluctuating frequency. The fluctuations are due to diffusion of molecules or microparticles along the resonator. They lead to broadening and change of shape of the…
A theoretical model of resonant hyper-Raman scattering by an ensemble of spherical semiconductor quantum dots has been developed. The electronic intermediate states are described as Wannier-Mott excitons in the framework of the envelope…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
We provide a computational method for quickly determining the correct distribution of optically active nanoparticles for a desired response. This is achieved by simulating the optical response of single nanoparticles and performing a…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
We investigate a random normal matrix model with eigenvalues forced to be in the droplet, the support of the equilibrium measure associated with an external field. For radially symmetric external fields, we show that the fluctuations of the…
We perform molecular dynamic simulations of liquid nanoparticles deposited on a disordered substrate. The motion of the nanoparticle is characterised by a 'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$), analysis…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
We investigate numerically the dynamics of shape and displacement fluctuations of two-dimensional flexible vesicles filled with active particles. At low concentration most of the active particles accumulate at the boundary of the vesicle…
We investigate the stability and softness of nuclei against quadrupole, octupole, and hexadecapole deformation. By applying the spherical Skyrme-force Hartree-Fock Bardeen-Cooper-Schrieffer quasi-particle random phase approximation, we…
After multiple scattering of quadrature-squeezed lights in a disordered medium, the quadrature amplitudes of the scattered modes present an excess noise above the shot-noise level [Opt. Expr. 14, 6919 (2006)]. A natural question is raised…
When subjected to monochromatic incident light a nanoparticle will emit light which then interferes with the incident beam. With sufficient contrast and sufficiently close to the particle this interference pattern may be recorded with a…
The plasmonic response of nanoparticles is exploited in many subfields of science and engineering to enhance optical signals associated with probes of nanoscale and subnanoscale entities. We develop a numerical algorithm based on previous…
Nanomechanical resonators offer important benefits for the sensing of physical stimuli such as the mass of an added molecule. To map out the local shape properties of the physical stimuli, such as the distribution of the mass density of a…
We use numerical simulations to understand how random deviations from the ideal spherical shape affect the ability of hard particles to form fcc crystalline structures. Using a system of hard spheres as a reference, we determine the…