Related papers: Large Orders for Self-Avoiding Membranes
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
We show that the average size of self-avoiding polygons (SAP) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We…
In this work we study the recently introduced octonionic duality for membranes. Restricting the self - duality equations to seven space dimensions, we provide various forms for them which exhibit the symmetries of the octonionic and…
We demonstrate in two minisuperspace models that a perturbation expansion of quasiclassical Euclidean gravity has a factorial dependence on the order of the term at large orders. This behavior indicates that the expansion is an asymptotic…
Four-dimensional quaternion-Kaehler metrics with an isometry are determined by solutions to the SU($\infty$) Toda equation. We set up a perturbation theory to construct approximate solutions to the latter which can be interpreted as…
We calculate the mean square amplitude of the shape fluctuation -- an equal-time correlation -- of an almost planar fluid membrane immersed in a near-critical binary fluid mixture. One fluid component is usually preferentially attracted by…
A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
We propose a model that leads to the formation of non-equilibrium finite-size domains in a biological membrane. Our model considers the active conformational change of the inclusions and the coupling between inclusion density and membrane…
We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to the general R-charge assignment to the matter fields. Though the…
The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with…
We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to…
We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At…
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\…
We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics…
Discrete symmetries of Calabi-Yau moduli spaces, generated by isomorphic flops, constrain the instanton expansion of the 4D $\mathcal{N}=2$ Type~IIA prepotential. We show that the Coxeter-invariant functions into which the prepotential…
We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical…
The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in…
We investigate the large-N limit of the BMN matrix model with classical bosonic membranes which have spherical topologies and spin inside the 11-dimensional maximally supersymmetric plane-wave background. First we classify all possible…