TY - JOUR
AB - In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.
AU - Fischer, Julian L
AU - Hensel, Sebastian
ID - 7489
JF - Archive for Rational Mechanics and Analysis
SN - 00039527
TI - Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension
ER -
TY - JOUR
AB - In plants, clathrin mediated endocytosis (CME) represents the major route for cargo internalisation from the cell surface. It has been assumed to operate in an evolutionary conserved manner as in yeast and animals. Here we report characterisation of ultrastructure, dynamics and mechanisms of plant CME as allowed by our advancement in electron microscopy and quantitative live imaging techniques. Arabidopsis CME appears to follow the constant curvature model and the bona fide CME population generates vesicles of a predominantly hexagonal-basket type; larger and with faster kinetics than in other models. Contrary to the existing paradigm, actin is dispensable for CME events at the plasma membrane but plays a unique role in collecting endocytic vesicles, sorting of internalised cargos and directional endosome movement that itself actively promote CME events. Internalized vesicles display a strongly delayed and sequential uncoating. These unique features highlight the independent evolution of the plant CME mechanism during the autonomous rise of multicellularity in eukaryotes.
AU - Narasimhan, Madhumitha
AU - Johnson, Alexander J
AU - Prizak, Roshan
AU - Kaufmann, Walter
AU - Tan, Shutang
AU - Casillas Perez, Barbara E
AU - Friml, Jiří
ID - 7490
JF - eLife
TI - Evolutionarily unique mechanistic framework of clathrin-mediated endocytosis in plants
VL - 9
ER -
TY - JOUR
AB - Endophytic fungi can be beneficial to plant growth. However, the molecular mechanisms underlying colonization of Acremonium spp. remain unclear. In this study, a novel endophytic Acremonium strain was isolated from the buds of Panax notoginseng and named Acremonium sp. D212. The Acremonium sp. D212 could colonize the roots of P. notoginseng, enhance the resistance of P. notoginseng to root rot disease, and promote root growth and saponin biosynthesis in P. notoginseng. Acremonium sp. D212 could secrete indole‐3‐acetic acid (IAA) and jasmonic acid (JA), and inoculation with the fungus increased the endogenous levels of IAA and JA in P. notoginseng. Colonization of the Acremonium sp. D212 in the roots of the rice line Nipponbare was dependent on the concentration of methyl jasmonate (MeJA) (2 to 15 μM) and 1‐naphthalenacetic acid (NAA) (10 to 20 μM). Moreover, the roots of the JA signalling‐defective coi1‐18 mutant were colonized by Acremonium sp. D212 to a lesser degree than those of the wild‐type Nipponbare and miR393b‐overexpressing lines, and the colonization was rescued by MeJA but not by NAA. It suggests that the cross‐talk between JA signalling and the auxin biosynthetic pathway plays a crucial role in the colonization of Acremonium sp. D212 in host plants.
AU - Han, L
AU - Zhou, X
AU - Zhao, Y
AU - Zhu, S
AU - Wu, L
AU - He, Y
AU - Ping, X
AU - Lu, X
AU - Huang, W
AU - Qian, J
AU - Zhang, L
AU - Jiang, X
AU - Zhu, D
AU - Luo, C
AU - Li, S
AU - Dong, Q
AU - Fu, Q
AU - Deng, K
AU - Wang, X
AU - Wang, L
AU - Peng, S
AU - Wu, J
AU - Li, W
AU - Friml, Jiří
AU - Zhu, Y
AU - He, X
AU - Du, Y
ID - 7497
JF - Journal of Integrative Plant Biology
SN - 1672-9072
TI - Colonization of endophyte Acremonium sp. D212 in Panax notoginseng and rice mediated by auxin and jasmonic acid
ER -
TY - JOUR
AU - Mazur, E
AU - Kulik, Ivan
AU - Hajny, Jakub
AU - Friml, Jiří
ID - 7500
JF - New Phytologist
SN - 0028-646x
TI - Auxin canalization and vascular tissue formation by TIR1/AFB-mediated auxin signaling in arabidopsis
ER -
TY - JOUR
AB - In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.
AU - Bossmann, Lea
AU - Pavlović, Nataša
AU - Pickl, Peter
AU - Soffer, Avy
ID - 7508
JF - Journal of Statistical Physics
SN - 0022-4715
TI - Higher order corrections to the mean-field description of the dynamics of interacting bosons
ER -
TY - JOUR
AB - In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,
where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0