Interpretation of the temperature dependence of equilibrium and rate constants

The objective of this review is to draw attention to potential pitfalls in attempts to glean mechanistic information from the magnitudes of standard enthalpies and entropies derived from the temperature dependence of equilibrium and rate constants for protein interactions. Problems arise because the minimalist model that suffices to describe the energy differences between initial and final states usually comprises a set of linked equilibria, each of which is characterized by its own energetics. For example, because the overall standard enthalpy is a composite of those individual values, a positive magnitude for AHO can still arise despite all reactions within the subset being characterized by negative enthalpy changes: designation of the reaction as being entropy driven is thus equivocal. An experimenter must always bear in mind the fact that any mechanistic interpretation of the magnitudes of thermodynamic parameters refers to the reaction model rather than the experimental system For the same reason there is little point in subjecting the temperature dependence of rate constants for protein interactions to transition-state analysis. If comparisons with reported values of standard enthalpy and entropy of activation are needed, they are readily calculated from the empirical Arrhenius parameters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor

The metallic state of high-temperature copper-oxide superconductors, characterized by unusual and distinct temperature dependences in the transport properties(1-4), is markedly different from that of textbook metals. Despite intense theoretical efforts(5-11), our limited understanding is impaired by our inability to determine experimentally the temperature and momentum dependence of the transport scattering rate. Here, we use a powerful magnetotransport probe to show that the resistivity and the Hall coefficient in highly doped Tl2Ba2CuO6+delta originate from two distinct inelastic scattering channels. One channel is due to conventional electron electron scattering; the other is highly anisotropic, has the same symmetry as the superconducting gap and a magnitude that grows approximately linearly with temperature. The observed form and anisotropy place tight constraints on theories of the metallic state. Moreover, in heavily doped non-superconducting La2-xSrxCuO4, this anisotropic scattering term is absent(12), suggesting an intimate connection between the origin of this scattering and superconductivity itself.

Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically trapped Fermi gas in the unitary limit. Our calculations compare Monte Carlo results with the equation of state of a uniform gas using three distinct perturbation schemes. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Pair correlations in a finite-temperature 1D Bose gas

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature “fermionization” through the measurement of the rates of two-body inelastic processes, such as photoassociation.

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants J1 and J2 on a lattice that interpolates between the limits of a square lattice (J1=0), a triangular lattice (J2=J1), and decoupled linear chains (J2=0). In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature Tp. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs2CuCl4 and Cs2CuBr4 and to a number of organic molecular crystals. We find that the former (Cs2CuCl4 and Cs2CuBr4) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Magnetic susceptibility of the normal-superconducting transition in high-purity single-crystal α-uranium

We report complex ac magnetic susceptibility measurements of a superconducting transition in very high-quality single-crystal alpha-uranium using microfabricated coplanar magnetometers. We identify an onset of superconductivity at Tapproximate to0.7 K in both the real and imaginary components of the susceptibility which is confirmed by resistivity data. A superconducting volume fraction argument, based on a comparison with a calibration YBa2Cu3O7-delta sample, indicates that superconductivity in these samples may be filamentary. Our data also demonstrate the sensitivity of the coplanar micro-magnetometers, which are ideally suited to measurements in pulsed magnetic fields exceeding 100 T.

Enhanced flow visualisation using near-resonant holographic interferometry

Holographic interferometry measurements have been performed on high-speed, high-temperature gas flows with a laser output tuned near a resonant sodium transition. The technique allows the detection and quantification of the sodium concentration in the flow. By controlling the laser detuning and seeded sodium concentration, we performed flow visualization in low-density flows that are not normally detectable with standard interferometry. The technique was also successfully used to estimate the temperature in the boundary layer of the flow over a flat plate.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Incubation of turtle eggs at different temperatures: Do embryos compensate for temperature during development?

Freshwater turtle eggs are normally subjected to fluctuations in incubation temperature during natural incubation. Because of this, developing embryos may make physiological adjustments to growth and metabolism in response to incubation at different temperatures. I tested this hypothesis by incubating eggs of the Brisbane river turtle Emydura signata under four different temperature regimes, constant temperatures of 24 degrees C and 31 degrees C throughout incubation, and two swapped-temperature treatments where incubation temperature was changed approximately halfway through incubation. Incubation at 31 degrees C took 42 d, and incubation at 24 degrees C look 78 d, with intermediate incubation periods for the swapped-temperature treatments. Hatchling mass, hatchling size, and total oxygen consumed during development were similar for all incubation regimes. The pattern of oxygen consumption during the last phase of incubation as reflected by rate of increase of oxygen consumption, peak oxygen consumption, and fall in oxygen consumption before hatching was determined solely by the incubation temperature during the last phase of incubation; that is, incubation temperature during the first phase of incubation had no influence on these factors. Thus there is no evidence of temperature compensation in growth or development during embryonic development of E. signata eggs.