Notes on Smooth and Singular Volumetric Growth

The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive property for which a smooth flux field exists, even if the property is not conserved. Singular flux fields are considered using the notion of a de Rham current. Writing a generalized balance law using the boundary of the current corresponding to a singular flux field, surface growth is unified with volumetric growth.Comment: 5 figure

Spectral estimates of the p-Laplace Neumann operator and Brennan's conjecture

In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂R2 . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings

Spectral estimates of the p-Laplace Neumann operator and Brennan's conjecture

In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂R2 . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings

Distortion of Mappings and Lq,pL_{q,p}-Cohomology

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are given

Continuum Kinematics with Incompatible-Compatible Decomposition

Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities, and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors which includes the standard elastic-plastic decomposition in plasticity

Mechanical and biocompatible properties of the poly(lactide-co-glycolide) matrices produced by antisolvent 3D printing

Three-dimensional scaffolds were made from a solution of poly(lactide-co-glycolide) mixed with tetraglycol using antisolvent 3D printing. The elastic properties and the structure of the obtained matrices were studied. MTT-test and staining with PKH-26, Calcein-AM, DAPI with subsequent fluorescence microscopy were used to study biological properties. The three-dimensional scaffolds had good mechanical properties. Young’s modulus value was 18±2 MPa, tensile strength was 0.43±0.05 MPa. The relative survival rate of cells after the first day was 99.58±2.28%, on the 14th day – 98.14±2.22%. The structure of the scaffold promoted cell adhesion and spreading on its surface. The poly(lactide-co-glycolide) matrices produced by antisolvent printing have high porosity, biocompatibility and good mechanical properties. It is allowed to use them in the future as a basis for personalized constructions for the replacement of extensive bone defects

Interaction of climate change with effects of conspecific and heterospecific density on reproduction

We studied the relationship between temperature and the coexistence of great titParus majorand blue titCyanistes caeruleus, breeding in 75 study plots across Europe and North Africa. We expected an advance in laying date and a reduction in clutch size during warmer springs as a general response to climate warming and a delay in laying date and a reduction in clutch size during warmer winters due to density-dependent effects. As expected, as spring temperature increases laying date advances and as winter temperature increases clutch size is reduced in both species. Density of great tit affected the relationship between winter temperature and laying date in great and blue tit. Specifically, as density of great tit increased and temperature in winter increased both species started to reproduce later. Density of blue tit affected the relationship between spring temperature and blue and great tit laying date. Thus, both species start to reproduce earlier with increasing spring temperature as density of blue tit increases, which was not an expected outcome, since we expected that increasing spring temperature should advance laying date, while increasing density should delay it cancelling each other out. Climate warming and its interaction with density affects clutch size of great tits but not of blue tits. As predicted, great tit clutch size is reduced more with density of blue tits as temperature in winter increases. The relationship between spring temperature and density on clutch size of great tits depends on whether the increase is in density of great tit or blue tit. Therefore, an increase in temperature negatively affected the coexistence of blue and great tits differently in both species. Thus, blue tit clutch size was unaffected by the interaction effect of density with temperature, while great tit clutch size was affected in multiple ways by these interactions terms.Peer reviewe

Variation in clutch size in relation to nest size in birds

Peer reviewe

Sobolev extension operators and Neumann eigenvalues

In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of of the first nontrivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem (initially proposed by J.~J.~Sylvester in 1857)