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Atomic force microscopy (AFM) is a key tool for characterising nanoscale structures, with functionalised tips now offering detailed images of the atomic structure. In parallel, AFM simulations using the particle probe model provide a…
Forces acting between an Atomic Force Microscope (AFM) tip and sample are three dimensional. Despite this, most AFM force measurements are confined to one or two dimensions. Extending AFM force measurements into three dimensions has…
Surface wettability has a huge influence on its functional properties. For example, to minimize smudging, surfaces should be able to repel oil droplets. To quantify surface wettability, the most common approach is to measure the contact…
A method is presented for the reconstruction of rotating monopole source distributions using acoustic pressures measured on a sideline parallel to the source axis. The method requires no \textit{a priori} assumptions about the source other…
The description of hydrodynamic interactions between a particle and the surrounding liquid, down to the nanometer scale, is of primary importance since confined liquids are ubiquitous in many natural and technological situations. In this…
This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as the distillation of flow matching models. Uniqueness of the…
Atomically-resolved imaging and force measurements using the atomic force microscope (AFM) are performed most commonly in a frequency-modulation (FM) mode. This has led to spectacular results, including direct observation of the atomic…
A novel method for measuring the surface coverage of randomly distributed cylindrical nanoparticles such as nanorods and nanowires, using atomic force microscopy (AFM), is presented. The method offers several advantages over existing…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
Tapping mode atomic force microscopy is a standard technique for inspection and analysis at the nanometer scale. The understanding of the non-linear dynamics of the system due to the tip sample interaction is an important prerequisite for a…
We report a systematic study to determine local elastic properties of surfaces combining atomic force microscope (AFM) with acoustic waves which is known as atomic force acoustic microscopy - AFAM. We describe the methodology of AFAM in…
Atomic force microscopy (AFM) is a well-known tool for studying surface roughness and to collect depth information about features on the top atomic layer of samples. By combining secondary ion mass spectroscopy (SIMS) with focused ion beam…
We study an inverse problem for Light Sheet Fluorescence Microscopy (LSFM), where the density of fluorescent molecules needs to be reconstructed. Our first step is to present a mathematical model to describe the measurements obtained by an…
We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force…
This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…
Stretchable conductors are of crucial relevance for emerging technologies such as wearable electronics, low-invasive bioelectronic implants or soft actuators for robotics. A critical issue for their development regards the understanding of…
Detection of dynamic surface displacements associated with local changes in material strain provides access to a number of phenomena and material properties. Contact resonance-enhanced methods of Atomic Force Microscopy (AFM) have been…
Amplitude-modulation atomic force microscopy (AM-AFM) measures nanoscale surface structures by detecting changes in the cantilever oscillation amplitude, contributing to materials research. AM-AFM can non-destructively observe fragile…
Molecular density functional theory is a powerful technique for efficiently computing the spatially and orientationally dependent equilibrium density of a molecular solvent around an arbitrary solute. This density encodes the detailed…
Atomic Force Microscopy (AFM) allows to reconstruct the topography of surface with a resolution in the nanometer range. The exceptional resolution attainable with the AFM makes this instrument a key tool in nanoscience and technology. The…