Related papers: Discrete-to-Continuum Limits of Long-Range Electri…
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…
We show that a model of interacting electrons in one dimension is able to explain the order of magnitude as well as the temperature dependence of the critical supercurrents recently measured in nanotube samples placed between…
Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a {\it single} surface nanobubble has been theoretically explained, i.e. contact line…
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite…
We theoretically study the interplay between electrical and mechanical properties of suspended, doubly clamped carbon nanotubes in which charging effects dominate. In this geometry, the capacitance between the nanotube and the gate(s)…
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties…
The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the…
We study a class of interacting particle systems in which $n$ signed particles move on the real line. At close range particles with the same sign repel and particles with opposite sign attract each other. The repulsion and attraction are…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We derive formulae for the electrostatic interaction between two long, rigid macromolecules that may have arbitrary surface charge patterns and cross at an arbitrary interaxial angle. We calculate the dependence of the interaction energy on…
In this thesis we study the lateral electrostatic interaction between a pair of non-identical, moderately charged colloidal particles trapped at an electrolyte interface in the limit of short inter-particle separations. Using a simplified…
We study the magnetic field dependence of the dielectric response of large cylindrical molecules such as nanotubes. When a field-induced level crossing takes place, an applied electric field causes a linear instead of the usual quadratic…
Atomic structures of nanomaterials are inherently dynamic, continuously reshaped through interactions with chemical species and external stimuli. Such dynamics are further amplified as the size and dimensionality of nanomaterials are…
We theoretically study the low-energy scattering of ultracold atoms by a dielectric nanosphere of silica glass levitated in a vacuum. The atom and dielectric surface interact via dispersion force of which strength sensitively depends on the…
In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach…
Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with…
Aequous dielectrics are ubiquitous in soft- and bio-nano matter systems. The theoretical description of such systems in terms of continuum (`macroscopic') theory remains a serious challenge. In this perspective we first review the existing…
The low-energy properties of two-dimensional ensembles of dipole-coupled magnetic nanoparticles are studied as function of structural disorder and particle coverage. Already small deviations from a square particle arrangement lift the…
Electromagnetic properties of periodic two-dimensional sub-wavelength structures consisting of closely-packed inclusions of materials with negative dielectric permittivity $\epsilon$ in a dielectric host with positive $\epsilon_h$ can be…
We derive an energy-based continuum limit for $\varepsilon$-graphs endowed with a general connectivity functional. We prove that the discrete energy and its continuum counterpart differ by at most $O(\varepsilon)$; the prefactor involves…