We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γlimit is also stable under volume constraint and various type of boundary conditions.

We provide an approximation result in the sense of Γ-convergence for energies of the form ˆ Ω Q1(e(u)) dx+ aH(Ju) + b ˆ Ju Q 1/2 0 ([u] νu) dH n−1, where Ω ⊂ Rn is a bounded open set with Lipschitz boundary, Q0 and Q1 are coercive quadratic forms on Mn×n sym , a, b are positive constants, and u runs in the space of fields SBD2(Ω) , i.e., it’s a special field with bounded deformation such that i...

The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

We show the Γ-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.

The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn-Hilliard/Modica-Mortola energy, there are additional ‘forces’ that prevent larg...

In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter ε, representing the interface thickness between the tumorous and non tumorous cells, tends to zero. More in particular, we analyze here a gradient-flow type model arising from a modification of the recently introduced model for tumor growth dynamics in...

The essential oil of Illicium simonsii fruit was obtained by hydrodistillation and analyzed by gas chromatography-mass spectrometry (GC-MS). A total of 40 components of the essential oil were identified. The principal compounds in I. simonsii fruit essential oil were β-caryophyllene (10.30%), δ-cadinene (9.52%), methyl eugenol (8.94), β-elemene (5.84%), and α-amorphene (5.20%). The essential oi...

Essential oils of Duguetia lanceolata barks, obtained at 2 (T2) and 4 h (T4), were identified by gas chromatography and gas chromatography/mass spectrometry. β-elemene (12.7 and 14.9%), caryophyllene oxide (12.4 and 10.7%) and β-selinene (8.4 and 10.4%) were the most abundant components in T2 and T4, respectively. The essential oils inhibited the growth of Staphylococcus aureus, Streptococcus p...

The Mikania genus has been known to possess numerous pharmacological activities. In the present study, we aimed evaluate interaction of 26 selected constituents species with (i) cyclooxygenase 2 (COX 2), (ii) human neutrophil elastase (HNE), (iii) lipoxygenase (LOX), matrix metalloproteinase ((iv) MMP and (v) 9), (vi) microsomal prostaglandin E synthase (mPGES 2) inhibitors using an in silico a...

The volatile oils from leaves of Michelia champaca L. collected bimonthly during one year (four times on the fifteenth day of January, March, May, July, September, and November 2004) were subjected to GC/FID and GC-MS analysis, from which thirteen components were identified. Additionally, part of the oil obtained from January collection was subjected to fractionation over silica gel soaked with...