Related papers: Global Small-Angle Scattering Data Analysis of Inv…
The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…
This paper presents a large-scale $ab$ $initio$ simulation study of amorphous silicon hydride ($a$-Si$_{\text{1-x}}$H$_{\text{x}}$) with an emphasis on the structure and properties of the material across a range of hydrogen concentration by…
Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…
Optical second-harmonic generation (SHG) is studied for the confined geometry of a circular cylindrical waveguide or optical fiber. A model situation of high symmetry is considered where the material with nonlinear susceptibility is…
We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in…
All-atom molecular dynamics simulations of 1,2-dimyristoyl-sn-glycerol-3-phosphocholine lipid membranes reveal a membrane phase transition dictated drastic growth in the interface water (IW) heterogeneity length scales. It acts as an…
Characterization of structural diversity within soft materials is key for engineering new materials for various applications. Small-angle scattering (SAS) is a widely used characterization technique that provides structural information in…
A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this…
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We present a minimal model for simulating dynamics of assorted lipid assemblies in a computationally efficient manner. Our model is particle-based and consists of coarse-grained beads put together on a modular platform to give generic…
In this work, we use a tempering-based adaptive particle filter to infer from a partially observed stochastic rotating shallow water (SRSW) model which has been derived using the Stochastic Advection by Lie Transport (SALT) approach. The…
An approach is presented for the inversion of simulated and experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a…
The scattering amplitude in the dual model with Mandelstam analyticity and trajectory $\alpha (s)=\alpha_{0}-\gamma \ln [ (1+\beta \sqrt{s_{0} -s})/(1+ \beta \sqrt{s_{0}})]$ is studied in the limit $s,|t|\to \infty, s/t=const.$ By using the…
A rigorous homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent effective admittivity with respect to the membrane…
In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation is introduced, and its integrability as an infinite dimensional Hamilton dynamic system is established. Motivated by the ideas of Ablowitz and Musslimani (2016…
$\bullet$ Multiscale model of inner-core anisotropy produced by hcp alloy deformation$\bullet$ 5 to 20% single-crystal elastic anisotropy and plastic deformation by pyramidal slip $\bullet$ Low-degree inner-core formation model with faster…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
We propose a simplified description of fluid adsorption on heterogenenous micropatterned substrates. Using this approach, we are able to rederive results obtained earlier using effective interfacial Hamiltonian methods and predict a number…