Applying the variational principle to (1+1)-dimensional quantum field theories

We extend the recently introduced continuous matrix product state variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the application of the variational procedure to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free of fermion doubling and sign problems. We illustrate the power of the formalism by studying the momentum occupation for free massive Dirac fermions and the chiral symmetry breaking in the Gross-Neveu model.     

Giant bubble pinch-off

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a downward jet. Only in the limiting case of large Froude numbers does the purely inertial scaling h(-logh)(1/4) proportional tau(1/2) for the neck radius h [J. M. Gordillo et al., Phys. Rev. Lett. 95, 194501 (2005)] become visible. For any finite Froude number the collapse is slower, and a second length scale, the curvature of the void, comes into play. Both length scales are found to exhibit power-law scaling in time, but with different exponents depending on the Froude number, signaling the nonuniversality of the bubble pinch-off.     

Classification of Some Optimal Ternary Linear Codes of Small Length

A classification is given of some optimal ternary linear codes of small length. Dimension 2 is classified for every minimum distance. Dimension 3, 4 and 5 is classified up to minimum distance 12. For higher dimension a classification is given where possible.     

Non-perturbative approach to the matrix model

We present a variational approach to calculate the vacuum energy of a hermitian matrix model. The approach generalizes a previously proposed non-perturbative technique (the 2PPI expansion) to fields which carry an additional tensor structure. The method works for any number of space-time dimensions and produces good results over the whole range of the coupling constant and the matrix order. We study the 0- and 1-dimensional case.     

Mixed-volume computation by dynamic lifting applied to polynomial system solving

The aim of this paper is to present a flexible approach for the efficient computation of the mixed volume of a tuple of polytopes. In order to compute the mixed volume, a mixed subdivision of the tuple of polytopes is needed, which can be obtained by embedding the polytopes in a higher-dimensional space, i.e., by lifting them. Dynamic lifting is opposed to the static approach. This means that one considers one point at a time and only fixes the value of the lifting function when the point really influences the mixed volume. Conservative lifting functions have been developed for this purpose. This provides us with a deterministic manipulation of the lifting for computing mixed volumes, which rules out randomness conditions. Cost estimates for the algorithm are given. The implications of dynamic lifting on polyhedral homotopy methods for the solution of polynomial systems are investigated and applications are presented.     

Functionalization of cotton with poly-NiPAAm/chitosan microgel: Part II. Stimuli-responsive liquid management properties

An innovative strategy for functional finishing of cotton involves application of stimuli-responsive surface modifying system based on temperature- and pH-responsive poly-NiPAAm/chitosan microgel. The stimuli-responsiveness implied to cotton is the consequence of swelling/collapse of the microgel particles incorporated to the fibre surface, which produces an active liquid management system. The performance of functionalized cotton fabric in terms of liquid management properties was assessed by choosing appropriate techniques (water uptake; thin-layer wicking; water retention capacity; and drying capability) and discussion of the results was based on the types of water that are expected to be present in hydrated cotton and stimuli-responsive microgel.     

Polyhedral end games for polynomial continuation

Bernshtein’s theorem provides a generically exact upper bound on the number of isolated solutions a sparse polynomial system can have in (ℂ^*)ⁿ, with ℂ^* = ℂ\{0}. When a sparse polynomial system has fewer than this number of isolated solutions some face system must have solutions in (ℂ^*)ⁿ. In this paper we address the process of recovering a certificate of deficiency from a diverging solution path. This certificate takes the form of a face system along with approximations of its solutions. We apply extrapolation to estimate the cycle number and the face normal. Applications illustrate the practical usefulness of our approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Nonexistence of Ternary [50,5,32] Codes

It is unknown (cf. Hill and Newton [8] or Hamada [3]) whether or not there exists a ternary [50,5,32] code meeting the Griesmer bound. The purpose of this paper is to prove the nonexistence of ternary [50,5,32] codes. Since there exists a ternary [51,5,32] code, this implies that n3(5,32) = 51, where n3(k,d) denotes the smallest value of n for which there exists a ternary [n,k,d] code.     

Nonlinear reduction for solving deficient polynomial systems by continuation methods

Summary Neither continuation methods, nor symbolic elimination methods can be directly applied to compute all finite solutions to polynomial systems, because the amount of computational time is mostly not proportional to the dimension of the system and to the number of finite solutions. The notion of S-polynomials is used to developed a reduction algorithm to lower the total degree of the deficient polynomial system, so that computing the solutions at infinity can be avoided. Applying the reduction algorithm before solving the system with continuation methods, yields a reliable solution method.