SO(5) superconductor in a Zeeman magnetic field: Phase diagram and thermodynamic properties

In this paper we present calculations of the SO(5) quantum rotor theory of high-T$_{c}$ superconductivity in Zeeman magnetic field. We use the spherical approach for five-component quantum rotors in three-dimensional lattice to obtain formulas for critical lines, free energy, entropy and specific heat and present temperature dependences of these quantities for different values of magnetic field. Our results are in qualitative agreement with relevant experiments on high-T$_{c}$ cuprates.Comment: 4 pages, 2 figures, to appear in Phys. Rev. B, see http://prb.aps.or

Transition in a numerical model of contact line dynamics and forced dewetting

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle $\theta_\Delta$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from $15^\circ$ to $110^\circ$ and capillary numbers from $0.00085$ to $0.2$ where the mesh size $\Delta$ is varied in the range of $0.0035$ to $0.06$ of the capillary length $l_c$. To interpret the results, we use Cox's theory which involves a microscopic distance $r_m$ and a microscopic angle $\theta_e$. In the numerical case, the equivalent of $\theta_e$ is the angle $\theta_\Delta$ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function $\phi$ so that $r_m = \Delta/\phi$ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on $\theta_\Delta$ and the viscosity ratio $q$. In the case of small $\theta_e$, we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large $\theta_e$ and arbitrary $q$ and express the critical capillary number as a function of $\theta_e$ and $r_m$. An analogy can be drawn between $r_m$ and the numerical slip length.Comment: This version of the paper includes the corrections indicated in Ref. [1

Relativity and the lead-acid battery

The energies of the solid reactants in the lead-acid battery are calculated ab initio using two different basis sets at non-relativistic, scalar relativistic, and fully relativistic levels, and using several exchange-correlation potentials. The average calculated standard voltage is 2.13 V, compared with the experimental value of 2.11 V. All calculations agree in that 1.7-1.8 V of this standard voltage arise from relativistic effects, mainly from PbO2 but also from PbSO4

TRANSIT TIME IN ITAJAÍ-AÇÚ RIVER ESTUARY

O Estuário do rio Itajaí-Açu é um estuário altamente estratificado, e apresenta durante a maior parte do ano uma proeminente cunha salina. Devido a esta característica foi possível aplicar o modelo de caixa, baseado no teorema hidrográfico de Knudsen, para se estimar o balanço salino e o tempo de trânsito das águas fluvial e marinha no estuário. Este modelo possibilita verificar o estado estático das condições de mistura no estuário e não deve ser confundido com as condições médias do estuário. Uma característica positiva deste modelo é o fato dele precisar de um numero pequeno de parâmetros, como perfil de salinidade, volume do estuário e dados de corrente, estes últimos estimados a partir de dados de descarga fluvial. Foram analisados sete dias de dados, compreendendo um ciclo completo de maré (sizígia-quadratura). Dados de velocidade vertical, estimados pelo modelo, mostraram que as condições de maré de sizígia causam um maior grau de mistura. Para confirmar isto foi definido um coeficiente de mistura dado pela razão do conteúdo de água fluvial pelo de água de mistura, o que comprovou tal padrão. Quanto ao tempo de transito, verificou-se que em situações de média descarga, cerca de 215 m3.s-1, o tempo de trânsito da água marinha foi três vezes maior do que o da água fluvial. Os valores estimados foram de 13.2 horas para a água fluvial e 50.7 horas para água marinha.The Itajaí-Açu estuary is classified as a highly stratified and presents most of the time a salt wedge. Considering this characteristic, it was used a box model, based on Knudsen hidrographic teorem, to estimate the salt balance and the transit time of fluvial and marine waters in this estuary. This model enables to verify the steady state of mixture conditions and should not be confused as the mean conditions of the estuary. A positive characteristic of this model is that it needs a small number of parameters such as salinity profiles, the estuary volume and currents data, being the latter estimated from river discharge. Seven days of data were assessed, comprising a half synodical cycle (spring-neap tide). Vertical velocities data, estimated by the model, showed that spring tide condition causes a more effective mixing. It was stated a ratio of content of fluvial water to the content of mixohaline water, which confirmed the early findings of intensification of mixing during spring tide period. The estimation of the transit time of fluvial and marine water in the estuary for medium discharge condition, ~ 215 m3.s-1, were 13.2 and 50.7 hours, respectively. It shows that the marine water spends 3 times more time in the estuary than the fluvial water

Surface Quality of a Work Material Influence on Vibrations in a Cutting Process

The problem of stability in the machining processes is an important task. It is strictly connected with the final quality of a product. In this paper we consider vibrations of a tool-workpiece system in a straight turning process induced by random disturbances and their effect on a product surface. Basing on experimentally obtained system parameters we have done the simulations using one degree of freedom model. The noise has been introduced to the model by the Langevin equation. We have also analyzed the product surface shape and its dependence on the level of noise.Comment: 12 pages, PDF of figures can be obtained from http://archimedes.pol.lublin.pl/~raf/graf/fpic.pd

Neel Order and Electron Spectral Functions in the Two-Dimensional Hubbard Model: a Spin-Charge Rotating Frame Approach

Using recently developed quantum SU(2)xU(1) rotor approach, that provides a self-consistent treatment of the antiferromagnetic state we have performed electronic spectral function calculations for the Hubbard model on the square lattice. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green's function in the space-time domain as the product CP^1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. As a result the problem of calculating the spectral line shapes now becomes one of performing the convolution of spin, charge and pseudo-fermion Green's functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.Comment: 16 pages, 5 figures, submitted to Phys. Rev.

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures