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There are various routes for deriving partial radial distribution functions of disordered systems from experimental diffraction (and/or EXAFS) data. Due to limitations and errors of experimental data, as well as to imperfections of the…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the…
The origin of friction force is a very old problem in physics, which goes back to Leonardo da Vinci or even older times. Extremely important from a practical point of view, but with no satisfactory explanation yet. Many models have been…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Traction Force Microscopy (TFM) computes the forces exerted at the surface of an elastic material by measuring induced deformations in volume. It is used to determine the pattern of the adhesion forces exerted by cells or by cellular…
In this work we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the 1-dimensional nonlinear Schrodinger equation whose nonlinear term presents a nonlinear defocusing strength that varies…
We demonstrate the application of Atomic Force Microscopy (AFM) based optical force microscopy to map the optical near-fields with nanometer resolution, limited only by the AFM probe geometry. We map the electric field distributions of…
Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such…
Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a…
This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density…
Atomic Force Microscopy (AFM) is a widely employed tool for micro-/nanoscale topographic imaging. However, conventional AFM scanning struggles to reconstruct complex 3D micro-/nanostructures precisely due to limitations such as incomplete…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
Interatomic-force measurements are regularly performed using frequency-modulation atomic force microscopy. This requires conversion of the observed shift in the resonant frequency of a force-sensing cantilever, to the actual force…
Over the past few decades, there has been a rapid improvement in computational power as well as techniques to simulate the real world phenomenon which has enabled us to understand the physics and develop new systems which outperform the…
Ultrasound Atomic Force Microscopy (US-AFM) has been used for subsurface imaging of nanostructures. The contact stiffness variations have been suggested as the origin of the image contrast. Therefore, to analyze the image contrast, the…
This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose a new algorithm to determine the inter-particle…