Symmetry-improved CJT effective action

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2)$\mathbb{O}(2)$ scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2)$\mathbb{O}(2)$ is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.     

On complete intersection toric ideals of graphs

We study the graphs G for which their toric ideals I _G are complete intersections. In particular, we prove that for a connected graph G such that I _G is a complete intersection all of its blocks are bipartite except for at most two. We prove that toric ideals of graphs which are complete intersections are circuit ideals. In this case, the generators of the toric ideal correspond to even cycles of G except of at most one generator, which corresponds to two edge disjoint odd cycles joint at a vertex or with a path. We prove that the blocks of these graphs satisfy the odd cycle condition. Finally, we characterize all complete intersection toric ideals of graphs which are normal.     

Organic–inorganic bonding in chitosan–silica hybrid networks: Physical properties

Novel biomaterials are needed for bone tissue repair with improved mechanical performance compared to classical bioceramics. The objective of this work was to characterize a hybrid filler material, which is capable to coat as a thin film porous scaffolds improving their mechanical properties for bone tissue engineering. The hybrid filler material is a blend of chitosan and silica network formed through in situ sol–gel using tetraethylortosilicate and 3‐glycidoxypropyltrimethoxysilane (GPTMS) as silica precursors. The hypothesis was that the epoxy ring of GPTMS could react with the amino groups of chitosan in acidic media while it is also reacting the siloxane groups of hydrolyzed silica precursors. The formation of the hybrid organic–inorganic network was assessed by different physical techniques revealing changes in molecular mobility and hydrophilicity upon chemical reaction. Finally, the cytotoxicity of the samples was also evaluated by MTT assay. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1391–1400     

Approximate dynamic programming for stochastic linear control problems on compact state spaces

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal policies usually cannot be computed, not even for instances of moderate size.     

The saddle point problem and the Manteuffel algorithm

In the last two decades, the augmented linear systems and the saddle point problems have been solved by many researchers who have used the conjugate gradient method or the generalized SOR iterative method and variants of them. In the latter class of methods, when the block \(A \in {\mathrm{I\!R}}^{m\times m}\) of the matrix coefficient \(\mathcal {A} = \left[ \begin{array}{cc} A &{} B \\ -B^T &{} 0\end{array}\right] \in {\mathrm{I\!R}}^{(m+n) \times (m+n)}\), \(m \ge n,\) of the linear system to be solved, is symmetric positive definite and \({\mathrm{rank}}(B) =r \le n\), convergence regions and optimal values of the parameters involved have been determined. In this work, we consider the block A to be nonsymmetric positive definite, \({\mathrm{rank}}(B) =r < n \), and use a two-level stationary iterative method whose main step is the linear second-order stationary iterative method for the solution of this class of problems. This method leads to the singular Manteuffel algorithm and the determination of its optimal parameters. As a byproduct, the optimal parameters of the Generalized Modified SSOR method in a particular case are also determined. Numerical examples verify our theoretical findings.     

Thermal transitions and dynamics in nanocomposite hydrogels

Hydrogels based on nanocomposites of statistical poly(hydroxyethyl acrylate-co-ethyl acrylate) and silica, prepared by simultaneous copolymerization and generation of silica nanoparticles by sol?Cgel process at various copolymer compositions and silica contents, characterized by a fine dispersion of filler, were investigated with respect to glass transition and polymer dynamics by dielectric techniques. These include thermally stimulated depolarization currents and dielectric relaxation spectroscopy, covering together broad ranges of frequency and temperature. In addition, equilibrium water sorption isotherms were recorded at room temperature (25?°C). Special attention was paid to the investigation of effects of silica on glass transition, polymer dynamics (secondary ?? and ?? _sw relaxations and segmental ?? relaxation), and electrical conductivity in the dry systems (xerogels) and in the hydrogels at various levels of relative humidity/water content. An overall reduction of molecular mobility is observed in the nanocomposite xerogels, in particular at high silica contents. Analysis of the results and comparison with previous work on similar systems enable to discuss this reduction of molecular mobility in terms of constraints to polymeric motion imposed by interfacial polymer?Cfiller interactions and by the formation of a continuous silica network interpenetrated with the polymer network at filler contents higher than about 15?wt%.     

Electronic spectroscopy and electronic structure of diatomic TiFe

Diatomic TiFe, a 12 valence electron molecule that is isoelectronic with Cr(2), has been spectroscopically investigated for the first time. In addition, the first computational study that includes the ground and excited electronic states is reported. Like Cr(2), TiFe has a (1)Σ(+) ground state that is dominated by the 1σ(2) 2σ(2) 1π(4) 1δ(4) configuration. Rotationally resolved spectroscopy has established a ground state bond length of 1.7024(3) A?, quite similar to that found for Cr(2) (r(0) = 1.6858 A?). Evidently, TiFe exhibits a high degree of multiple bonding. The vibronic spectrum is highly congested and intense to the blue of 20?000 cm(-1), while two extremely weak band systems, the [15.9](3)Π(1) ← X (1)Σ(+) and [16.2](3)Π(0+) ← X (1)Σ(+) systems, are found in the 16?000-18?500 cm(-1) region. The bond lengths, obtained by inversion of the B(e) (') values, and vibrational frequencies of the two upper states are nearly identical: 1.886?A? and 344 cm(-1) for [15.9](3)Π(1) and 1.884 A? and 349 cm(-1) for [16.2](3)Π(0+). The measured spin-orbit splitting of the (3)Π state is consistent with its assignment to the 1σ(2) 2σ(2) 1π(4) 1δ(3) 2π(1) configuration, as is also found in the ab initio calculations.     

Opportunities for Particles and Particle Suspensions to Experience Enhanced Transport in Porous Media: A Review

Transport in Porous Media - The possibility of broaching, or the release of fluids at the seafloor due to a damaged or faulty well, is a hazard that must be assessed in the well permitting process....