Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Carbonation of photocatalytic aluminosilicate cement composites: Evolution of self-cleaning and radiative cooling properties

This study aims to understand the impact of carbonation on the photocatalytic self-cleaning and radiative cooling properties of autoclaved cement composites. The composites are prepared with varying silica contents and sources, with and without alumina addition under autoclave conditions. The phase composition, microstructure, optical properties, and photocatalytic self-cleaning performance are systematically characterized and analyzed. Outdoor measurements are conducted to validate the cooling performance of the material under ambient conditions. Cracking behaviors during autoclave/carbonation treatments and the performance degradation in functionalities upon carbonation are observed. The cement/nanosilica/alumina ternary system demonstrates the best overall performance, considering productibility during autoclave curing, effectiveness, and carbonation durability of functionalities. C-A-S-H minerals, mainly Al-Foshagite, in this system, serve as precursors for the generation of γ-Al2O3 upon carbonation, mitigating the deterioration of photocatalytic properties. The findings are expected to provide new insights for the development and engineering practice of functional cementitious materials for durable cooling applications

Self-cleaning performance of autoclaved photocatalytic cement pastes:Insights into phase composition, microstructure and aluminum incorporation in C–S–H

This study attempts to comprehend mechanisms that enhance the photocatalytic properties of autoclaved cementitious pastes. The photocatalytic self-cleaning performance, phase composition, microstructure, optical properties, and silicate chain properties are characterized and analyzed. The results indicate that the silica source and alumina play significant roles in the evolution of phase composition and microstructure, which consequently affects the photocatalytic self-cleaning performance. The impacts of in-situ generated cement hydrates on the photocatalytic performance of cementitious materials are discussed for the first time, as well as the mechanisms governing the different morphologies of C–S–H crystals with the addition of different oxides. For the first time, the role of aluminum incorporation in the C–S–H network and major factors at different stages on the photocatalytic performance of cementitious materials are discussed. Finally, a systematic understanding of the photocatalytic properties of autoclaved cementitious materials is established. These results provide insights into the development of photocatalytic cementitious materials with tailored performances.</p

Modeling of torsion stress giant magnetoimpedance in amorphous wires with negative magnetostriction

A model describing the influence of torsion stress on the giant magnetoimpedance in amorphous wires with negative magnetostriction is proposed. The wire impedance is found by means of the solution of Maxwell equations together with the Landau-Lifshitz equation, assuming a simplified spatial distribution of the magnetoelastic anisotropy induced by the torsion stress. The impedance is analyzed as a function of the external magnetic field, torsion stress and frequency. It is shown that the magnetoimpedance ratio torsion dependence has an asymmetric shape, with a sharp peak at some value of the torsion stress. The calculated field and stress dependences of the impedance are in qualitative agreement with results of the experimental study of the torsion stress giant magnetoimpedance in Co-based amorphous wires.Comment: 17 pages, 5 figure

The electronic specific heat in the pairing pseudogap regime

When pairing correlations in a quasi two dimensional electron system induce a pseudogap in the single particle density of states, the specific heat must also contain a sizeable pair contribution. The theoretically calculated specific heat for such a system is compared to the experimental results of Loram and his collaborators for underdoped YBa_2Cu_3O_{6+x} and La_{2-x}Sr_{x}CuO_4 samples. The size and doping dependence of the extracted pseudogap energy scale for both materials is comparable to the values obtained from a variety of other experiments.Comment: 4 pages, 5 eps figure

Magnetism in systems with various dimensionality: A comparison between Fe and Co

A systematic ab initio study is performed for the spin and orbital moments and for the validity of the sum rules for x-ray magnetic circular dichroism for Fe systems with various dimensionality (bulk, Pt-supported monolayers and monatomic wires, free-standing monolayers and monatomic wires). Qualitatively, the results are similar to those for the respective Co systems, with the main difference that for the monatomic Fe wires the term in the spin sum rule is much larger than for the Co wires. The spin and orbital moments induced in the Pt substrate are also discussed.Comment: 4 page

Current distribution and giant magnetoimpedance in composite wires with helical magnetic anisotropy

The giant magnetoimpedance effect in composite wires consising of a non-magnetic inner core and soft magnetic shell is studied theoretically. It is assumed that the magnetic shell has a helical anisotropy. The current and field distributions in the composite wire are found by means of a simultaneous solution of Maxwell equations and the Landau-Lifshitz equation. The expressions for the diagonal and off-diagonal impedance are obtained for low and high frequencies. The dependences of the impedance on the anisotropy axis angle and the shell thickness are analyzed. Maximum field sensitivity is shown to correspond to the case of the circular anisotropy in the magnetic shell. It is demonstrated that the optimum shell thickness to obtain maximum impedance ratio is equal to the effective skin depth in the mahnetic material.Comment: 23 pages, 7 figure

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation $$-\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3,$$ where $\Omega$ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega$ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty$ if $\Omega$ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.Comment: 29 pages, 8 figure

Physical origin of the buckling in CuO2_2: Electron-phonon coupling and Raman spectra

It is shown theoretically that the buckling of the CuO$_{2}$ planes in certain cuprate systems can be explained in terms of an electric field across the planes which originates from different valences of atoms above and below the plane. This field results also in a strong coupling of the Raman-active out-of-phase vibration of the oxygen atoms ($B_{1g}$ mode) to the electronic charge transfer between the two oxygens in the CuO$_{2}$ plane. Consequently, the electric field can be deduced from the Fano-type line shape of the $B_{1g}$ phonon. Using the electric field estimated from the electron-phonon coupling the amplitude of the buckling is calculated and found to be in good agreement with the structural data. Direct experimental support for the idea proposed is obtained in studies of YBa$_{2}$Cu$_{3}$O$_{6+x}$ and Bi$_{2}$Sr$_{2}$(Ca$_{1-x}$Y$_{x}$)Cu$_{2}$O$_{8}$ with different oxygen and yttrium doping, respectively, including antiferromagnetic samples. In the latter compound, symmetry breaking by replacing Ca partially by Y leads to an enhancement of the electron-phonon coupling by an order of magnitude.Comment: 12 pages, 4 figures, and 1 tabl

Mucormycosis in Australia: Contemporary epidemiology and outcomes

Mucormycosis is the second most common cause of invasive mould infection and causes disease in diverse hosts, including those who are immuno-competent. We conducted a multicentre retrospective study of proven and probable cases of mucormycosis diagnosed between 2004–2012 to determine the epidemiology and outcome determinants in Australia. Seventy-four cases were identified (63 proven, 11 probable). The majority (54.1%) were caused by Rhizopus spp. Patients who sustained trauma were more likely to have non-Rhizopus infections relative to patients without trauma (OR 9.0, p 0.001, 95% CI 2.1–42.8). Haematological malignancy (48.6%), chemotherapy (42.9%), corticosteroids (52.7%), diabetes mellitus (27%) and trauma (22.9%) were the most common co-morbidities or risk factors. Rheumatological/autoimmune disorders occurred in nine (12.1%) instances. Eight (10.8%) cases had no underlying co-morbidity and were more likely to have associated trauma (7/8; 87.5% versus 10/66; 15.2%; p <0.001). Disseminated infection was common (39.2%). Apophysomyces spp. and Saksenaea spp. caused infection in immuno-competent hosts, most frequently associated with trauma and affected sites other than lung and sinuses. The 180-day mortality was 56.7%. The strongest predictors of mortality were rheumatological/autoimmune disorder (OR = 24.0, p 0.038 95% CI 1.2–481.4), haematological malignancy (OR = 7.7, p 0.001, 95% CI 2.3–25.2) and admission to intensive care unit (OR = 4.2, p 0.02, 95% CI 1.3–13.8). Most deaths occurred within one month. Thereafter we observed divergence in survival between the haematological and non-haematological populations (p 0.006). The mortality of mucormycosis remains particularly high in the immuno-compromised host. Underlying rheumatological/autoimmune disorders are a previously under-appreciated risk for infection and poor outcome