Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

Multidrug resistance and cancer: the role of the human ABC transporter ABCG2

A variety of human cancers become resistant or are intrinsically resistant to treatment with conventional chemotherapy, a phenomenon called multidrug resistance. This broad-based resistance results in large part, but not solely, from overexpression of members of the ATP-binding cassette (ABC) superfamily of membrane transporters, including P-glycoprotein, various members of the multidrug resistance associated proteins (MRPs), and ABCG2, also known as MXR1, BCRP, and ABCP. When overexpressed in cell lines, ABCG2 has the ability to confer high levels of resistance to anthracyclines, mitoxantrone, bisantrene, and the camptothecins topotecan and SN-38. This review focuses on the discovery, the biochemistry and the normal physiology of human ABCG2, a novel ABC half transporter expressed abundantly in placenta, as well as in liver, intestine and stem cells. ABCG2 may serve a protective function by preventing toxins from entering cells as well as potentially playing a role in regulating stem cell differentiation. We also discuss the involvement of ABCG2 in multidrug resistance in cancer, especially with regard to acute myeloid leukemia. The mechanism by which substrates are recognized by ABCG2 and how the energy of ATP hydrolysis is transduced into transport remain elusive. A complete understanding of the mechanism and biological function of ABCG2 will be important for understanding its normal physiology as well as potentially for the development of novel chemotherapeutic treatment strategies.     

Route to Lambda in conformally coupled phantom cosmology

In this Letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system and analyze it on a invariant 2-dimensional submanifold. Then the concordance FRW model with the cosmological constant Λ   is a global attractor situated on a 2-dimensional invariant space. We also study the behaviour near this attractor, which can be approximated by the dynamics of the linearized part of the system. We demonstrate that trajectories of the conformally coupled phantom scalar field with a simple quadratic potential crosses the cosmological constant barrier infinitely many times in the phase space. The universal behaviour of the scalar field and its potential is also calculated. We conclude that the phantom scalar field conformally coupled to gravity gives a natural dynamical mechanism of concentration of the equation of state coefficient around the magical value weff=−1$w_{\mathrm{eff}}=-1$. We demonstrate route to Lambda through the infinite times crossing the weff=−1$w_{\mathrm{eff}}=-1$ phantom divide.     

Dissipative or conservative cosmology with dark energy?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property—acceleration—is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a one-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We characterize the class of dark energy models that admit late time de Sitter attractor solution in terms of the potential function of corresponding conservative system. We argue that inclusion of dissipation effects makes the model more realistic because of its structural stability. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the χ² function which is illustrated by residuals and χ² levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of χ² statistic are comparable for both the viscous model and ΛCDM model. The Bayesian information criteria are used to compare the models with different power-law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the ΛCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.     

The minimum degree distance of graphs of given order and size

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.     

Twister quintessence scenario

We study generic solutions in a non-minimally coupled to gravity scalar field cosmology. It is shown that dynamics for both canonical and phantoms scalar fields with the potential can be reduced to the dynamical system from which the exact forms for an equation of the state parameter can be derived. We have found the stationary solutions of the system and discussed their stability. Within the large class of admissible solutions we have found a non-degenerate critical points and we pointed out multiple attractor type of trajectory travelling in neighborhood of three critical points at which we have the radiation dominating universe, the barotropic matter dominating state and finally the de Sitter attractor. We have demonstrated the stability of this trajectory which we call the twister solution. Discovered evolutional path is only realized if there exist the non-minimal coupling constant. We have found simple duality relations between twister solutions in phantom and canonical scalar fields in the radiation domination phase. For the twister trajectory we have found an oscillating regime of approaching the de Sitter attractor.     

Poisson brackets,Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.     

The structure of Lennard-Jones dimerizing spheres near a hard wall from the nonuniform wertheim Ornstein-Zernike equation

A dimerizing model of Lennard-Jones particles near a hard wall is studied using the inhomogeneous or second order Wertheim Ornstein-Zernike equation and the inhomogeneous associative Percus-Yevick closure. We investigate the influence of the degree of dimerization on the shape of the density profiles and on inhomogeneous pair correlation functions. This work was supported in parts by KBN of Poland (the Grant No. 3T09A 06210) and by Cray Research, Inc., of Mexico under its University Research and Development Grant Program. Garcia.     

Invertible architectures from amphiphilic polyesters

We synthesized and characterized novel amphiphilic polyesters with both hydrophilic and hydrophobic functionalities. The polyesters are soluble in organic and aqueous media and reveal the formation of inverse architectures whose behavior could be correlated to their chemical structure. We foresee that the amphiphilic properties of the polyesters reported here are obviously the basis of new architectures both in solution and on the solid surfaces, which could be used in a broad range of applications. The described synthesis of the copolymers is very simple and is based on commercially available products. That makes this approach attractive in various uses.     

Reforming of oxygenates for H2 production: correlating reactivity of ethylene glycol and ethanol on Pt(111) and Ni/Pt(111) with surface d-band center

The dehydrogenation and decarbonylation of ethylene glycol and ethanol were studied using temperature programmed desorption (TPD) on Pt(111) and Ni/Pt(111) bimetallic surfaces, as probe reactions for the reforming of oxygenates for the production of H2 for fuel cells. Ethylene glycol reacted via dehydrogenation to form CO and H2, corresponding to the desired reforming reaction, and via total decomposition to produce C(ad), O(ad), and H2. Ethanol reacted by three reaction pathways, dehydrogenation, decarbonylation, and total decomposition, producing CO, H2, CH4, C(ad), and O(ad). Surfaces prepared by deposition of a monolayer of Ni on Pt(111) at 300 K, designated Ni-Pt-Pt(111), displayed increased reforming activity compared to Pt(111), subsurface monolayer Pt-Ni-Pt(111), and thick Ni/Pt(111). Reforming activity was correlated with the d-band center of the surfaces and displayed a linear trend for both ethylene glycol and ethanol, with activity increasing as the surface d-band center moved closer to the Fermi level. This trend was opposite to that previously observed for hydrogenation reactions, where increased activity occurred on subsurface monolayers as the d-band center shifted away from the Fermi level. Extrapolation of the correlation between activity and the surface d-band center of bimetallic systems may provide useful predictions for the selection and rational design of bimetallic catalysts for the reforming of oxygenates.