We reveal a connection between the incompressibility method and the Lovász local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated on the example of van der Waerden numbers. It applies to lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.

This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin’s famous wave function. We investigate a model...

We treat the problem of constructmg exact théories of rods and shells for thm mcom pressible bodies We employ a systematic method that consists m imposmg constramts to reduce the number of degrees of freedom df each cross section to a finit e number We show that it is very difficult to produce théories that exactly preserve the mcompressibihty and we show that it is impossible to do so for naïv...

Let p be a prime integer, F a field of characteristic not p, T the norm torus of a degree p extension field of F , and E a T -torsor over F such that the degree of each closed point on E is divisible by p (a generic T -torsor has this property). We prove that E is p-incompressible. Moreover, all smooth compactifications of E (including those given by toric varieties) are p-incompressible. The m...

This paper presents a new methodology, apparatus design, and the experimental results of ongoing research into the measurement of the mechanical properties of musculoskeletal tissue at the cellular level. A microchamber was constructed that provides a controlled hydrostatic pressure environment for these cells where optical sectioning, via epifluorescence microscopy, was used to acquire volume ...

We establish a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions. When the deformation parameter is a third root of unity, the representation degenerates and the wave functions coincide with the domain wall boundary condition partition function appearing in the conjecture of A.V. Razumov and Y.G...

Abstract We present a coupled model for brittle materials based on the ordinary state-based peridynamics. The peridynamics theory is suitable describing plastic incompressibility problem and has good application prospects in fracture damage simulation of materials. material with compressive load-bearing capacity greater than tensile characteristics incompressibility, which consistent scope mech...

The quest to create superhard materials rarely strays from the use of high-pressure synthetic methods, which typically require gigapascals of applied pressure. We report that rhenium diboride (ReB2), synthesized in bulk quantities via arc-melting under ambient pressure, rivals materials produced with high-pressure methods. Microindentation measurements on ReB2 indicated an average hardness of 4...

Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the perfo...

Estimation of motion has many applications in fluid analysis. A lot of work has been carried out using Particle Image Velocimetry (PIV) to design experiments which capture and measure the flow motion using 2D images. Recent technological advances allow capturing 3D PIV image sequences of moving particles. In this paper, we deal with incompressible fluid flows which are a large class of physical...