Related papers: DNA toroid condensation as analytic solutions
DNA-spools, structures in which DNA is wrapped and helically coiled onto itself or onto a protein core are ubiquitous in nature. We develop a general theory describing the non-equilibrium behavior of DNA-spools under linear tension. Two…
The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have…
The existence of attractions between like-charged colloids immersed in ionic solution have been discovered in recent experiments. This phenomenon contradicts the predictions of DLVO theory and indicates a failure of mean field theory. We…
This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground-state density matrix is a fixed-point of the DMET map for…
Tethered particle motion is an experimental technique to monitor conformational changes in single molecules of DNA in real time, by observing the position fluctuations of a micrometer-size particle attached to the DNA. This article reviews…
By exploiting the exquisite selectivity of DNA hybridization, DNA-Coated Colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the…
In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred renewed interest in discrete element method (DEM) modeling of frictional contact. Force…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…
Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory…
We prove that linear and weakly non-linear run and tumble equations converge to a unique steady state solution with an exponential rate in a weighted total variation distance. In the linear setting, our result extends the previous results…
The influence of tension on DNA looping has been studied both experimentally and theoretically in the past. However, different theoretical models have yielded different predictions, leaving uncertainty about their validity. We briefly…
We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod like chain, involving two elastic constants, the bending and the twist rigidities. We show that this model is singular and needs a small…
Several processes in the cell, such as gene regulation, start when key proteins recognise and bind to short DNA sequences. However, as these sequences can be hundreds of million times shorter than the genome, they are hard to find by simple…
The strength of the spin-orbit interaction relevant to transport in a low dimensional structure depends critically on the relative geometrical arrangement of current carrying orbitals. Recent tight-binding orbital models for spin transport…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
Long range charge transfer experiments in DNA oligomers and the subsequently measured -- and very diverse -- transport response of DNA wires in solid state experiments exemplifies the need for a thorough theoretical understanding of charge…
The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x)…
We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…