Can dark matter be a Bose-Einstein condensate?

We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.Comment: 20 pages, 7 figures, accepted for publication in JCAP, references adde

HMG1A and PPARG are differently expressed in the liver of fat and lean broilers

The expression of nine functional candidates for QT abdominal fat weight and relative abdominal fat content was investigated by real-time polymerase chain reaction (PCR) in the liver, adipose tissue, colon, muscle, pituitary gland and brain of broilers. The high mobility group AT-hook 1 (HMG1A) gene was up-regulated in liver with a ratio of means of 2.90 (P ≤ 0.01) in the «fatty» group (relative abdominal fat content 3.5 ± 0.18%, abdominal fat weight 35.4 ± 6.09 g) relative to the «lean» group (relative abdominal fat content 1.9 ± 0.56%, abdominal fat weight 19.2 ± 5.06 g). Expression of this gene was highly correlated with the relative abdominal fat content (0.70, P ≤ 0.01) and abdominal fat weight (0.70, P ≤ 0.01). The peroxisome proliferator-activated receptor gamma (PPARG) gene was also up-regulated in the liver with a ratio of means of 3.34 (P ≤ 0.01) in the «fatty» group relative to the «lean» group. Correlation of its expression was significant with both the relative abdominal fat content (0.55, P ≤ 0.05) and the abdominal fat weight (0.57, P ≤ 0.01). These data suggest that the HMG1A and PPARG genes were candidate genes for abdominal fat deposition in chickens. Searching of rSNPs in regulatory regions of the HMG1A and PPARG genes could provide a tool for gene-assisted selection

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

Dark energy problem: from phantom theory to modified Gauss-Bonnet gravity

The solution of dark energy problem in the models without scalars is presented. It is shown that late-time accelerating cosmology may be generated by the ideal fluid with some implicit equation of state. The universe evolution within modified Gauss-Bonnet gravity is considered. It is demonstrated that such gravitational approach may predict the (quintessential, cosmological constant or transient phantom) acceleration of the late-time universe with natural transiton from deceleration to acceleration (or from non-phantom to phantom era in the last case).Comment: LaTeX 8 pages, prepared for the Proceedings of QFEXT'05, minor correctons, references adde

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Evaluation of the fibroblast growth factor system as a potential target for therapy in human prostate cancer

Overexpression of fibroblast growth factors (FGFs) has been implicated in prostate carcinogenesis. FGFs function via their high-affinity interactions with receptor tyrosine kinases, FGFR1–4. Expression of FGFR1 and FGFR2 in prostate cancer (CaP) was not found to be associated with clinical parameters. In this report, we further investigated for abnormal FGFR expression in prostate cancer and explore their significance as a potential target for therapy. The expression levels of FGFR3 and FGFR4 in CaP were examined and corroborated to clinical parameters. FGFR3 immunoreactivity in benign prostatic hyperplasia (BPH) and CaP (n=26 and 57, respectively) had similar intensity and pattern. Overall, FGFR4 expression was significantly upregulated in CaP when compared to BPH. A significant positive correlation between FGFR4 expression and Gleason score was noted: Gleason score 7–10 tumours compared to BPH (P<0.0001, Fisher's exact test), Gleason score 4–6 tumours compared to BPH (P<0.0004), and Gleason 7–10 compared to Gleason 4–6 tumours (P<0.005). FGFR4 overexpression was associated with an unfavourable outcome with decreased disease-specific survival (P<0.04, log rank test). FGF-induced signalling is targeted using soluble FGF receptor (sFGFR), potent inhibitor of FGFR function. We have previously shown that sFGFR expression via a replication-deficient adenoviral vector (AdlllcRl) suppresses in vitro FGF-induced signalling and function in human CaP DU145 cells. We tested the significance of inhibiting FGF function along with conventional therapeutic modalities in CaP, and confirmed synergistic effects on in vitro cell growth (proliferation and colony formation) by combining sFGFR expression and treatment with either Paclitaxel (Taxol®) or γ-irradiation. In summary, our data support the model of FGF system as valid target for therapy in CaP

Two-dimensional finite element simulation of fracture and fatigue behaviours of alumina microstructures for hip prosthesis

This paper describes a two-dimensional (2D) finite element simulation for fracture and fatigue behaviours of pure alumina microstructures such as those found at hip prostheses. Finite element models are developed using actual Al2O3 microstructures and a bilinear cohesive zone law. Simulation conditions are similar to those found at a slip zone in a dry contact between a femoral head and an acetabular cup of hip prosthesis. Contact stresses are imposed to generate cracks in the models. Magnitudes of imposed stresses are higher than those found at the microscopic scale. Effects of microstructures and contact stresses are investigated in terms of crack formation. In addition, fatigue behaviour of the microstructure is determined by performing simulations under cyclic loading conditions. It is shown that crack density observed in a microstructure increases with increasing magnitude of applied contact stress. Moreover, crack density increases linearly with respect to the number of fatigue cycles within a given contact stress range. Meanwhile, as applied contact stress increases, number of cycles to failure decreases gradually. Finally, this proposed finite element simulation offers an effective method for identifying fracture and fatigue behaviours of a microstructure provided that microstructure images are available

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ&gt; 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r

Coupled dark energy: Towards a general description of the dynamics

In dark energy models of scalar-field coupled to a barotropic perfect fluid, the existence of cosmological scaling solutions restricts the Lagrangian of the field \vp to p=X g(Xe^{\lambda \vp}), where X=-g^{\mu\nu} \partial_\mu \vp \partial_\nu \vp /2, $\lambda$ is a constant and $g$ is an arbitrary function. We derive general evolution equations in an autonomous form for this Lagrangian and investigate the stability of fixed points for several different dark energy models--(i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and (iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed points (\Omega_\vp=1) with an accelerated expansion in all models irrespective of the presence of the coupling $Q$ between dark energy and dark matter. These fixed points are always classically stable for a phantom field, implying that the universe is eventually dominated by the energy density of a scalar field if phantom is responsible for dark energy. When the equation of state w_\vp for the field \vp is larger than -1, we find that scaling solutions are stable if the scalar-field dominant solution is unstable, and vice versa. Therefore in this case the final attractor is either a scaling solution with constant \Omega_\vp satisfying 0<\Omega_\vp<1 or a scalar-field dominant solution with \Omega_\vp=1.Comment: 21 pages, 5 figures; minor clarifications added, typos corrected and references updated; final version to appear in JCA