AbstractsPhysics

Charged polymers are critical components of biological systems. DNA, F-actin, and bacteriophages are some examples of highly charged polymers. Because of their size, complexity, and of the long-range forces involved, full computer simulations can only be used for short times. Even standard theoretical approaches, such as mean-field theory, predict qualitatively wrong results.We seek to determine how parallel pairs of flexible like-charged polymers behave. We use minimal models to represent the polymers, and determine three particular behaviors: 1) How and when the polymers exhibit like-charged attraction. 2) Whether deformations away from a straight line are stable or unstable. 3) If allowed to evolve freely, what long-term structures would form.We represent our pair of infinite parallel charged polymers as a string of point charges linked with a spring potential. Counterions are represented by free point charges. With this system, we perform Monte Carlo simulations to find the following results:* Given two straight chains at fixed separation R, we reproduce the attractive interaction seen in other systems (real and simulated).* We find that the attraction decreases with temperature, lending support to the Wigner crystal model of this interaction.* We find a typical ground-state configuration, and calculate the interaction directly.* We find an expression that fits the force curve for a wide range of distances.* Using the force curve, we develop a simple approach to estimate the stability of the chains against small deformations.* Given wavelength deformations, we determine via simulations which modes decay and which grow, using three different methods. (linear stability analysis).* Initializing the system in the most unstable modes, we determine the structures formed in four cases: rigid, flexible-planar, flexible-free, and helical.* We find that flexible polyelectrolytes tend strongly towards a 1/f noise profile, when allowed to move freely at finite temperature.In summary, we developed and studied a minimal model of flexible polyelectrolytes, and investigated many of the core features of this system. Polymères chargés sont des éléments essentiels des systèmes biologiques. ADN, F-actine, et bactériophages sont des exemples de polymères fortement chargés. En raison de leur taille, de la complexité et des forces à longue portée impliqués, les simulations informatiques complets ne peuvent être utilisés pour de courtes durées. Même les approches théoriques standards (comme la théorie du champ moyen) prédisent des résultats qualitativement erronées.Nous cherchons à déterminé comment les paires parallèles de polymères comme -chargées flexibles se comportent. Nous utilisons des modèles minimaux pour représenter les polymères, et de déterminer trois comportements particuliers: 1) comment et quand les polymères attirent (attraction comme chargée). 2) Si les déformations au départ de la ligne droite sont stables ou instables. 3) Si a permis d'évoluer librement, ce que les structures à long terme feraient.Nous représentons…