Total energies from variational functionals of the Green function and the renormalized four-point vertex

We derive variational expressions for the grand potential or action in terms of the many-body Green function $G$ which describes the propagation of particles and the renormalized four-point vertex $\Gamma$ which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the $\Xi$-functional which plays a role analogously to the usual $\Phi$-functional studied by Baym (G.Baym, Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in many-body systems. We show that any $\Xi$-derivable theory is also $\Phi$-derivable and therefore respects the conservation laws. We further set up a computational scheme to obtain accurate total energies from our variational functionals without having to solve computationally expensive sets of self-consistent equations. The input of the functional is an approximate Green function $\tilde{G}$ and an approximate four-point vertex $\tilde{\Gamma}$ obtained at a relatively low computational cost. The variational property of the functional guarantees that the error in the total energy is only of second order in deviations of the input Green function and vertex from the self-consistent ones that make the functional stationary. The functionals that we will consider for practical applications correspond to infinite order summations of ladder and exchange diagrams and are therefore particularly suited for applications to highly correlated systems. Their practical evaluation is discussed in detail.Comment: 21 pages, 10 figures. Physical Review B (accepted

Crossover behavior for long reptating polymers

We analyze the Rubinstein-Duke model for polymer reptation by means of density matrix renormalization techniques. We find a crossover behavior for a series of quantities as function of the polymer length. The crossover length may become very large if the mobility of end groups is small compared to that of the internal reptons. Our results offer an explanation to a controversy between theory, experiments and simulations on the leading and subleading scaling behavior of the polymer renewal time and diffusion constant.Comment: 4 Pages, RevTeX, and 4 PostScript figures include

Reduction in mesenchymal stem cell numbers in premature aging DNA repair deficient TTD mice

Background: Mice carrying mutations in DNA repair genes often show signs of accelerated ageing and therefore can be used as a model system to study age related diseases like osteoporosis. It has been shown that TTD mice, carrying a mutation in the nucleotide excision repair gene XPD (xeroderma pigmentosa group D), display features of ageing related osteoporosis as well as adipose tissue hypoplasia. Since both cell types involved, osteoblasts as well as adipocytes, arise from the same mesenchymal stem cell population, the aim of the current project was to study the number, proliferation and differentiation potential of these cells in TTD compared to wild type (WT) mice. This might provide us with useful information concerning the mechanism behind age-related osteoporosis and the loss of adipose tissue.Methods: Bone marrow from old TTD and WT mice was cultured under osteogenic or adipogenic conditions and analysed for alkaline phosphatase activity (ALP), mineralisation (osteoblast) and lipid deposition (adipocyte).Results: Under osteogenic conditions the number of ALP-positive colonies after 9 and 14 days of culture was significantly decreased (p=0.02) in TTD compared to WT mice. The rate at which new ALP-positive colonies are formed between day 9 and day 14 of culture has not changed between TTD and WT mice, indicating that the decrease in colony number is not due to a delay in differentiation. Mineralisation of ALP-positive colonies did not seem to be affected, with a borderline significant decrease on day 14 at the onset of mineralisation but no significant changes on day 21 of culture. Lipid deposition was strongly reduced in TTD compared to WT mice (p=0.01) after 35 days of culture.Conclusions: The observed reduction in osteoblast and adipocyte differentiation indicates a reduction of mesenchymal stem cell numbers in TTD mice. This reduction in mesenchymal stem cell numbers and the corresponding decline in osteoblast differentiation could explain the premature osteoporotic features observed in TTD mice. In line with this, the reduction of mesenchymal stem cells and adipocyte differentiation may underlie the adipose tissue hypoplasia observed in TTD mice

Ensemble Theory for Force Networks in Hyperstatic Granular Matter

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution $P(f)$. For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a non-invertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting $P(f)$'s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a new perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.Comment: 17 pages, 17 figure

Sorting living mesenchymal stem cells using a TWIST1 RNA-based probe depends on incubation time and uptake capacity

Bone marrow derived mesenchymal stromal cells (BMSCs) are multipotent progenitors of particular interest for cell-based tissue engineering therapies. However, one disadvantage that limit their clinical use is their heterogeneity. In the last decades a great effort was made to select BMSC subpopulations based on cell surface markers, however there is still no general consensus on which markers to use to obtain the best BMSCs for tissue regeneration. Looking for alternatives we decided to focus on a probe-based method to detect intracellular mRNA in living cells, the SmartFlare technology. This technology does not require fixation of the cells and allows us to sort living cells based on gene expression into functionally different populations. However, since the technology is available it is debated whether the probes specifically recognize their target mRNAs. We validated the TWIST1 probe and demonstrated that it specifically recognizes TWIST1 in BMSCs. However, differences in probe concentration, incubation time and cellular uptake can strongly influence signal specificity. In addition we found that TWIST1high expressing cells have an increased expansion rate compared to TWIST1low expressing cells derivedfrom the same initial population of BMSCs. The SmartFlare probes recognize their target gene, however for each probe and cell type validation of the protocol is necessary

Phase Coexistence of a Stockmayer Fluid in an Applied Field

We examine two aspects of Stockmayer fluids which consists of point dipoles that additionally interact via an attractive Lennard-Jones potential. We perform Monte Carlo simulations to examine the effect of an applied field on the liquid-gas phase coexistence and show that a magnetic fluid phase does exist in the absence of an applied field. As part of the search for the magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase coexistence curves at large dipole moments, $\mu$. The critical temperature is found to depend linearly on $\mu^2$ for intermediate values of $\mu$ beyond the initial nonlinear behavior near $\mu=0$ and less than the $\mu$ where no liquid-gas phase coexistence has been found. For phase coexistence in an applied field, the critical temperatures as a function of the applied field for two different $\mu$ are mapped onto a single curve. The critical densities hardly change as a function of applied field. We also verify that in an applied field the liquid droplets within the two phase coexistence region become elongated in the direction of the field.Comment: 23 pages, ReVTeX, 7 figure