Mott insulator high T-c bipolaronic superconductor transition in cuprates - Discussion

All ‘undoped’ cuprates are antiferromagnetic Mott insulators. We argue that with doping they remain to be insulators including the ‘overdoped’ samples. Hence, there is no clear dividing line between non–metallic cuprates and high–temperature superconductors. Based on the generic Hamiltonian including the electron–phonon interaction and the direct Coulomb repulsion the ground state of doped cuprates is shown to be a charged 2e Bose liquid of small bipolarons. A theory of the normal state transport of copper oxides is developed. The temperature dependence of the resistivity and of the Hall effect agrees remarkably well with the experimental data in La2–xSrxCuO4 for the entire temperature regime including unusual ‘logarithmic’ low–temperature region. The violation of Kohler's rule in magnetoresistivity is explained. The resistive and thermodynamic superconducting transitions in a magnetic field are quantitatively described.

The melting and solidification of nanoscale Bi particles embedded in a glassy and crystalline matrix

We report the formation of an amorphous phase in nanosized Pi particles embedded in an Al-based glassy alloy matrix. High-resolution electron microscopy (HREM) has been used to show that the particles contain crystalline and amorphous portions. A depression of the melting point by more than 100 K of the crystalline portion of the Pi particles was found by differential scanning calorimetric studies and by in-situ electron microscopy using a heating stage. The same techniques established the absence of an amorphous phase in the particles when the matrix is crystallized. It is shown that the formation of the amorphous phase and the depression of the melting point cannot be explained by the pressure developed by the volume change during solidification in this constrained system.

J. B. S. Haldane, Ernst Mayr and the Beanbag Genetics Dispute

Starting from the early decades of the twentieth century, evolutionary biology began to acquire mathematical overtones. This took place via the development of a set of models in which the Darwinian picture of evolution was shown to be consistent with the laws of heredity discovered by Mendel. The models, which came to be elaborated over the years, define a field of study known as population genetics. Population genetics is generally looked upon as an essential component of modern evolutionary theory. This article deals with a famous dispute between J. B. S. Haldane, one of the founders of population genetics, and Ernst Mayr, a major contributor to the way we understand evolution. The philosophical undercurrents of the dispute remain relevant today. Mayr and Haldane agreed that genetics provided a broad explanatory framework for explaining how evolution took place but differed over the relevance of the mathematical models that sought to underpin that framework. The dispute began with a fundamental issue raised by Mayr in 1959: in terms of understanding evolution, did population genetics contribute anything beyond the obvious? Haldane's response came just before his death in 1964. It contained a spirited defense, not just of population genetics, but also of the motivations that lie behind mathematical modelling in biology. While the difference of opinion persisted and was not glossed over, the two continued to maintain cordial personal relations.

Icosahedral quasicrystalline and hexagonal approximant phases in the Al-Mn-Be alloy system

We report the formation of a primitive icosahedral quasicrystal with increased stability in Al Mn-Be alloys close to the compound Al15Mn13Be2, by melt spinning and injection casting. The crystal structure of this compound was unknown. We show that in as-cast as well as heat treated condition the intermetallic phase H1 has a hexagonal structure with lattice parameters a = 1.2295 run and c = 2.4634 nm. The space group is P6(3)/mmc In the injection-cast samples, the quasicrystal coexists with another closely related hexagonal phase H2 with a = 1.2295 nm and c = 1.2317 nm with a possible space group of P6/mmm. This phase exhibits specific orientation relationships with the icosahedral quasicrystal given by [0001](hex)//2f(QC) and [01 (1) over bar0](hex)//5f(QC) where 2f(QC) and 5f(QC) represent twofold and fivefold axes respectively. Electron diffraction patterns from both phases exhibit a close resemblance to the quasicrystalline phase. It is shown that the H1 phase is closely related to mu-Al4Mn with the same e parameter while the a parameter is reduced by tau. Following Kreiner and Franzen, it is postulated that both structures (H1 and H2) can be understood by a simple hexagonal packing of I13 clusters.

The role of sustainable agriculture and renewable-resource management in reducing greenhouse-gas emissions and increasing sinks in China and India

This paper contains an analysis of the technical options in agriculture for reducing greenhouse-gas emissions and increasing sinks, arising from three distinct mechanisms: (i) increasing carbon sinks in soil organic matter and above-ground biomass; (ii) avoiding carbon emissions from farms by reducing direct and indirect energy use; and (iii) increasing renewable-energy production from biomass that either substitutes for consumption of fossil fuels or replaces inefficient burning of fuelwood or crop residues, and so avoids carbon emissions, together with use of biogas digesters and improved cookstoves. We then review best-practice sustainable agriculture and renewable-resource-management projects and initiatives in China and India, and analyse the annual net sinks being created by these projects, and the potential market value of the carbon sequestered. We conclude with a summary of the policy and institutional conditions and reforms required for adoption of best sustainability practice in the agricultural sector to achieve the desired reductions in emissions and increases in sinks. A review of 40 sustainable agriculture and renewable-resource-management projects in China and India under the three mechanisms estimated a carbon mitigation potential of 64.8 MtC yr(-1) from 5.5 Mha. The potential income for carbon mitigation is $324 million at $5 per tonne of carbon. The potential exists to increase this by orders of magnitude, and so contribute significantly to greenhouse-gas abatement. Most agricultural mitigation options also provide several ancillary benefits. However, there are many technical, financial, policy, legal and institutional barriers to overcome.

An extended Cahn-Hilliard model for interfaces with cubic anisotropy

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

On limiting cases in the flexure of simply supported regular polygonal plates

Limiting solutions are derived for the flexure of simply supported many-sided regular polygons, as the number of sides is increased indefinitely. It is shown that these solutions are different from those for simply supported circular plates. For axisymmetric loading, circular plate solutions overestimate the deflexions and the moments by significant factors.

Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

The Future of Computation

The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words may be subjective, yet it is fairly clear that this is what all living organisms--from bacteria to human beings--do in their life time. Indeed, this can be adopted as the information theoretic definition of life. Over billions of years, biological evolution has experimented with a wide range of physical systems for acquiring, processing and communicating information. We are now in a position to make the principles behind these systems mathematically precise, and then extend them as far as laws of physics permit. Therein lies the future of computation, of ourselves, and of life.

XXVI. The relation between thermo-optic and piezo-optic phenomena in crystals

It is pointed out that the change in refractive index with temperature of a crystal is different from what is calculated from the accompanying change in volume and the piezo-optic coefficients. The difference, which is a pure temperature effect, is explained as being due to the change in polarizability of the atoms produced by a change in the amplitude of vibration. The polarizability (α) can be expanded as a Taylor series in the changes of the distance (r) between the atoms and it is found that while the piezo-optic coefficient depends only on ∂α/∂r, the pure temperature effect is a function of ∂ 2 a/∂r 2. Making use of the experimental data, the values of a and its first two derivatives can be determined. These values are foundto be of the same order as those deduced from the intensities of Rayleigh and Raman scattering of light. The theory predicts that dn/dT should vary as the coefficient of cubical expansion at different temperatures and this is verified to be true. Finally, calculations are made of the thermo- and piezo-optic coefficients, considering the electrostatic interaction between the atoms. These do not adequately explain the observed facts, since no provision is made for the distortion of electron atmospheres around the atoms and the consequent changes in polarizability.