Related papers: Stability analysis of kinked DNA in $\mathcal{F}(K…
Bending of DNA from a straight rod to a circular form in presence of any of the mono-, di-, tri- or tetravalent counterions has been simulated in strong Coulomb coupling environment employing a previously developed energy minimization…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We calculate the equation of state of DNA under tension for the case that the DNA features loops. Such loops occur transiently during DNA condensation in the presence of multivalent ions or sliding cationic protein linkers. The…
While the behavior of double stranded DNA at mesoscopic scales is fairly well understood, less is known about its relation to the rich mechanical properties in the base-pair scale, which is crucial, for instance, to understand DNA-protein…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
In this paper we consider the anharmonic corrections to the anisotropic elastic rod model for DNA. Our model accounts for the difference between the bending energies of positive and negative rolls, which comes from the asymmetric structure…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer…
A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase…
Thin dielectric elastomers with compliant electrodes exhibit various types of instability under the action of electromechanical loading. Guided by the thermodynamically-based formulation of Fosdick and Tang (J. Elasticity 88, 255-297,…
We propose a new simple model for DNA denaturation bases on the pendulum model of Englander\cite{A1} and the microscopic model of Peyrard {\it et al.},\cite{A3} so called "combined model". The main parameters of our model are: the coupling…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
We examine the Stillinger-Weber analysis of the potential energy landscape for its stability and conclude that it does not provide a stable description of the system as the free energy slope and curvature vanish simultaneously. An…
Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…
We consider a chain of free electrons with periodically switched dimerization and study the entanglement entropy of a segment with the remainder of the system. We show that it evolves in a stepwise manner towards a value proportional to the…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating…
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge…