Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Epigenetic modifier balances Mapk and Wnt signalling in differentiation of goblet and Paneth cells

Differentiation and lineage specification are controlled by cooperation of growth factor signalling. The involvement of epigenetic regulators in lineage specification remains largely elusive. Here, we show that the histone methyltransferase Mll1 prevents intestinal progenitor cells from differentiation, whereas it is also involved in secretory lineage specification of Paneth and goblet cells. Using conditional mutagenesis in mice and intestinal organoids, we demonstrate that loss of Mll1 renders intestinal progenitor cells permissive for Wnt-driven secretory differentiation. However, Mll1-deficient crypt cells fail to segregate Paneth and goblet cell fates. Mll1 deficiency causes Paneth cell-determined crypt progenitors to exhibit goblet cell features by unleashing Mapk signalling, resulting in increased numbers of mixed Paneth/goblet cells. We show that loss of Mll1 abolishes the pro-proliferative effect of Mapk signalling in intestinal progenitor cells and promotes Mapk-induced goblet cell differentiation. Our data uncover Mll1 and its downstream targets Gata4/6 as a regulatory hub of Wnt and Mapk signalling in the control of lineage specification of intestinal secretory Paneth and goblet cells

Bulk and Interfacial Shear Thinning of Immiscible Polymers

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear rate dependence of the interfacial viscosity is consistent with a shorter effective chain length $s^*$ that also describes the width of the interface. This $s^*$ is independent of chain length $N$ and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate.Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of $N$ and consistent with the bulk behavior for chains of length $s^*$. The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing $N$, while shear induced changes at the ends of chains are independent of $N$.Comment: 8 pages, 8 figure

Interfaces in Diblocks: A Study of Miktoarm Star Copolymers

We study AB$_n$ miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by implementing a numerically exact self-consistent field theory to probe the phase diagram and the shape of the AB interface.Comment: 12 pages, 11 included figure

The epigenetic regulator Mll1 is required for Wnt-driven intestinal tumorigenesis and cancer stemness

Wnt/β-catenin signaling is crucial for intestinal carcinogenesis and the maintenance of intestinal cancer stem cells. Here we identify the histone methyltransferase Mll1 as a regulator of Wnt-driven intestinal cancer. Mll1 is highly expressed in Lgr5(+) stem cells and human colon carcinomas with increased nuclear β-catenin. High levels of MLL1 are associated with poor survival of colon cancer patients. The genetic ablation of Mll1 in mice prevents Wnt/β-catenin-driven adenoma formation from Lgr5(+) intestinal stem cells. Ablation of Mll1 decreases the self-renewal of human colon cancer spheres and halts tumor growth of xenografts. Mll1 controls the expression of stem cell genes including the Wnt/β-catenin target gene Lgr5. Upon the loss of Mll1, histone methylation at the stem cell promoters switches from activating H3K4 tri-methylation to repressive H3K27 tri-methylation, indicating that Mll1 sustains stem cell gene expression by antagonizing gene silencing through polycomb repressive complex 2 (PRC2)-mediated H3K27 tri-methylation. Transcriptome profiling of Wnt-mutated intestinal tumor-initiating cells reveals that Mll1 regulates Gata4/6 transcription factors, known to sustain cancer stemness and to control goblet cell differentiation. Our results demonstrate that Mll1 is an essential epigenetic regulator of Wnt/β-catenin-induced intestinal tumorigenesis and cancer stemness

Study of Blume-Emery-Griffiths model by a modified Bethe-Peierls method

We present here a study of the Blume-Emery-Griffiths (BEG) model for general spins using a modified Bethe-Peierls (BP) method calling it the Bethe-Peierls-Lines (BPL) method, incorporating the well known Lines approximation. We compare our results of BPL as well as BP methods for the ferro-to para-magnetic transition temperatures T-c with those available from other theories such as the Correlated-Effective-Field Theory (CEFT), Cluster Variation Method (CVM) and the Monte-Carlo (MC) method. We find that our BPL method gives results for variation of T-c with the single-ion uniaxial anisotropy (D) and biquadratic interaction (J') coefficients close to those obtained by CVM method for spin S = 1 on a honeycomb lattice. We also find that the BPL results are in good agreement for the cubic lattice for S = 3/2 and J' = 0 with those of the MC results, and for S = 1 and J' = -0.5J with those of the CVM results. For these three dimensional lattices our BPL method gives the correct reentrant behaviour for negative values of J'. We also compare our BP and BPL results for magnetic susceptibility with those of the CEFT for S = 3/2 and 3 nearest neighbours and find fairly good agreement for D > 0

Study of spinels using the BPW method

We present a study of a group of B-site spinel ferrimagnetic compounds having magnetic properties dominated by strong ferromagnetic interactions, using a modified Bethe-Peierls-Weiss (BPW) method. We obtain the exchange parameters by studying the transition temperature and the inverse susceptibility curves. We use a method for obtaining the exchange constants using the ratio between the transition temperatures obtained by the Weiss molecular field theory and a more advanced theory, such as high temperature expansion, and compare the ratio with the experimental data. We also study the inverse magnetic susceptibility curves which, for the case of dominant ferromagnetic interactions, are linear in the high temperature limit and have nonlinear behaviour near the transition temperature. In particular, we study systems such as MCr(2)X(4), where M = Cd,Hg and X = S,Se, which are ferrimagnetic spinels, for which we find excellent fits to the experimental magnetic susceptibility data using the modified BPW method

Constant coupling cluster method

In this paper, we present a new method along the spirit of the constant coupling (CC) method for a pair, but now extended to a cluster of spins. We shall call this the constant coupling cluster (CCC) method. It is known that the CC approximation can be obtained as an approximation from the cluster expansion method. This gives us some justification for the use of this approximation. We present a comparative study of the present CCC method with the Bethe-Peierls-Weiss (BPW) and CC method. We find that it does not have the defects of the BPW method nor does it have the defects of the CC method and yet it is easily amenable for applications to complicated magnetic structures, which require multisublattice description