arXiv subjects

Joseph Rudnick

Publications and source records attributed to Joseph Rudnick.

62 records · Page 4Linked to original sources

arXiv1998

Avoided Critical Behavior in O(n) Systems

Long-range frustrating interactions, even if their strength is infinitesimal, can give rise to a dramatic proliferations of ground or near-ground states. As a consequence, the ordering temperature can exhibit a discontinuous drop as a function of the frustration. A simple model of the doped Mott insulator, where the short-range tendency of the holes to phase separate competes with long-range Coulomb effects, exhibits this "avoided critical" behavior. This model may serve as a paradigm for many other systems.

cond-mat.stat-mech↗

arXiv1998

DNA-Protein Cooperative Binding through Long-Range Elastic Coupling

Cooperativity plays an important role in the action of proteins bound to DNA. A simple, mechanical mechanism for cooperativity, in the form of a tension-mediated interaction between proteins bound to DNA at two different locations is proposed. These proteins are not in direct physical contact. DNA segments intercalating bound proteins are modeled as a Worm-Like Chain, which is free to deform in two dimensions. The tension-controlled protein-protein interaction is the consequence of two effects produced by the protein binding. The first is the introduction of a bend in the host DNA and the second is the modification of the bending modulus of the DNA in the immediate vicinity of the bound protein. The interaction between two bound proteins may be either attractive or repulsive, depending on their relative orientation on the DNA. Applied tension controls both the strength and the range of protein-protein interactions in this model. Properties of the cooperative interaction are discussed, along with experimental implications.

cond-mat.soft↗

arXiv1998

The effective potential, critical point scaling and the renormalization group

The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary $ϕ^4$ system, can be used to extract the effective potential. All scaling features are included in the process.

cond-mat.stat-mech↗

arXiv1997

Cluster Distribution in Mean-Field Percolation: Scaling and Universality

The partition function of the finite $1+ε$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are manifest, including scaling behavior and the emergence of the spanning cluster. The predictions are compared with simulations. Agreement is found to be good, although convergence between theory and numerical results as the system size is increased is, in some cases, unaccountably slow.

cond-mat.stat-mech↗

arXiv1997

Conformations of Circular DNA

We examine the elastic model of short circular DNA. We obtain analytic expressions for configurations, elastic energy, twist and linking number of our solutions. We find the onset of the plectonemic transition. We suggest ways to use our formalism to describe other elastic models, and to improve the current finite-element-analysis methods. We estimate the effect of thermodynamic fluctuations.

cond-mat.soft↗

arXiv1996

Conformations of Linear DNA

We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition.

cond-mat.soft↗

arXiv1995

Wulff Construction for Deformable Media

A domain in a Langmuir monolayer can be expected to have a shape that reflects the textural anisotropy of the material it contains. This paper explores the consequences of XY-like ordering. It is found that an extension of the Wulff construction allows for the calculation of two-dimensional domain shapes when each segment of the perimeter has an energy that depends both on its orientation and its location. This generalized Wulff construction, and newly-derived exact expressions for the order parameter texture in a circular domain, lead to results for the shape of a large domain. The most striking result is that under general conditions such domains will inevitably develop cusps. We show that the onset of a cusp is mathematically related to a phase transition. The present approach is equivalent to a Landau mean-field version of the theory.

cond-mat↗

arXiv1994

Shape of domains in two-dimensional systems: virtual singularities and a generalized Wulff construction

This is a report on the derivation and application of a generalized version of the Wulff construction in two dimensions. The construction is used to find the shape of a domain containing an XY-like order parameter. In such a domain the energy per unit length of a segment of the bounding curve depends not only on the orientation of the segment, but also on the segment's position, and this is why the Wulff construction must be generalized. When the domain is circular in shape we find that the problem of finding the texture that minimizes the bulk and boundary energies is exactly solvable in certain important cases. Using the generalized Wulff construction and the exact textures, describable in terms of virtual singularities, we find that, given reasonable assumptions concerning the from of the boundary energy, the domain will necessarily develop a cusp if it is sufficiently large. This result is in qualitative agreement with recent experimental observations.

cond-mat↗