Related papers: Flory Exponents from a Self-Consistent Renormaliza…
We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…
We perform numerical simulations of an active fully flexible self-avoiding polymer as a function of the quality of the embedding solvent described in terms of an effective monomer-monomer interaction. Specifically, by extracting the Flory…
We study polymers attached to spherical (circular) or paraboloidal (parabolic) probes in three (two) dimensions. Both self-avoiding and random walks are examined numerically. The behavior of a polymer of size $R_0$ attached to the tip of a…
Based on transfer matrix techniques and finite size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact…
Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is…
Polymer translocation through a nano-pore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
In this paper, we define the recurrence and "non-wandering" for decompositions. The following inclusion relations hold for codimension one foliations on closed $3$-manifolds: $\{$minimal$\} \sqcup \{$compact$\}$ $\subsetneq$ $\{$pointwise…
A cornerstone of modern polymer physics is the `Flory ideality hypothesis' which states that a chain in a polymer melt adopts `ideal' random-walk-like conformations. Here we revisit theoretically and numerically this pivotal assumption and…
We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose…
We study the number of irreducible factors (over $\mathbb{Q}$) of the $n$th iterate of a polynomial of the form $f_r(x) = x^2 + r$ for rational $r$. When the number of such factors is bounded independent of $n$, we call $f_r(x)$…
We construct polynomial automorphisms with wandering Fatou components. The four-dimensional automorphisms $H$ lie in a one-parameter family, depending on the parameter $\delta \in \mathbb C \setminus \{0\}$, and as $\delta \rightarrow 0$…
We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better…
The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a…
The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N…
We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and…
We consider the growth of a polymer layer on a flat surface in a good solvent by in-situ polymerization. This is viewed as a modified form of diffusion-limited aggregation without branching. We predict theoretically the formation of a…
Let $\mathcal{F}$ be written as $ f^{*}(\mathcal{G})$, where $\mathcal{G}$ is a $1$-dimensional foliation on $ {\mathbb P^{n-1}}$ and $f:{\mathbb P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local stability results…
We perform molecular-dynamics simulations for polymer melts of the coarse-grained polyvinyl alcohol model that crystallizes upon slow cooling. To establish the properties of its high temperature liquid state as a reference point, we…
The equilibrium structure and dynamics of a single polymer chain in a thermal solvent is by now well-understood in terms of scaling laws. Here we consider a polymer in a bacterial bath, i.e. in a solvent consisting of active particles which…