Analytic calculation of energy transfer and heat flux in a one-dimensional system

In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nature of the Fourier law for the model, and the nonlinear dependence of the rate of mechanical work on the stationary drift velocity of the tagged particle, are analyzed and elucidated.Comment: 17 pages including title pag

Reply to comment on "Simple one-dimensional model of heat conduction which obeys Fourier's law"

In this reply we answer the comment by A. Dhar (cond-mat/0203077) on our Letter "Simple one dimensional model of heat conduction which obeys Fourier's law" (Phys. Rev. Lett. 86, 5486 (2001), cond-mat/0104453)Comment: 1 pag., 1 fi

The Structure of Barium in the hcp Phase Under High Pressure

Recent experimental results on two hcp phases of barium under high pressure show interesting variation of the lattice parameters. They are here interpreted in terms of electronic structure calculation by using the LMTO method and generalized pseudopotential theory (GPT) with a NFE-TBB approach. In phase II the dramatic drop in c/a is an instability analogous to that in the group II metals but with the transfer of s to d electrons playing a crucial role in Ba. Meanwhile in phase V, the instability decrease a lot due to the core repulsion at very high pressure. PACS numbers: 62.50+p, 61.66Bi, 71.15.Ap, 71.15Hx, 71.15LaComment: 29 pages, 8 figure

Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses. We correct several claims in the recent literature based on much smaller simulations. Both for boundary conditions with two heat baths at different temperatures at both ends and from heat current autocorrelations in equilibrium we find heat conductivities kappa to diverge with the number N of particles. These depended very strongly on the mass ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33. This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that the hard-point gas with periodic boundary conditions is not chaotic in the usual sense and discuss why the system, when kept out of equilibrium, leads nevertheless to energy dissipation and entropy production.Comment: 4 pages (incl. 5 figures), RevTe

A simple one-dimensional model of heat conduction which obeys Fourier's law

We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR

Velocity Correlations, Diffusion and Stochasticity in a One-Dimensional System

We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a non-vanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a $t^{-3}$ tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.Comment: 22 files, 2 eps figures. Submitted to PR

Low temperature spin diffusion in the one-dimensional quantum O(3)O(3) nonlinear σ\sigma-model

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $O(3)$ non-linear $\sigma$-model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.Comment: 4 pages including 3 eps-figures, Revte

Ab Initio Calculation of Crystalline Electric Fields and Kondo Temperatures in Ce-Compounds

We have calculated the band-$f$ hybridizations for Ce$_x$La$_{1-x}$M$_3$ compounds ($x=1$ and $x\rightarrow 0$; M=Pb, In, Sn, Pd) within the local density approximation and fed this into a non-crossing approximation for the Anderson impurity model applied to both dilute and concentrated limits. Our calculations produce crystalline electric field splittings and Kondo temperatures with trends in good agreement with experiment and demonstrate the need for detailed electronic structure information on hybridization to describe the diverse behaviors of these Ce compounds.Comment: 13 pages(RevTeX), 3 Postscript figure

Femoral Neck External Size but not aBMD Predicts Structural and Mass Changes for Women Transitioning Through Menopause

The impact of adult bone traits on changes in bone structure and mass during aging is not well understood. Having shown that intracortical remodeling correlates with external size of adult long bones led us to hypothesize that ageâ related changes in bone traits also depend on external bone size. We analyzed hip dualâ energy Xâ ray absorptiometry images acquired longitudinally over 14 years for 198 midlife women transitioning through menopause. The 14â year change in bone mineral content (BMC, R2â =â 0.03, pâ =â 0.015) and bone area (R2â =â 0.13, pâ =â 0.001), but not areal bone mineral density (aBMD, R2â =â 0.00, pâ =â 0.931) correlated negatively with baseline femoral neck external size, adjusted for body size using the residuals from a linear regression between baseline bone area and height. The dependence of the 14â year changes in BMC and bone area on baseline bone area remained significant after adjusting for race/ethnicity, postmenopausal hormone use, the 14â year change in weight, and baseline aBMD, weight, height, and age. Women were sorted into tertiles using the baseline bone areaâ height residuals. The 14â year change in BMC (pâ =â 0.009) and bone area (pâ =â 0.001) but not aBMD (pâ =â 0.788) differed across the tertiles. This suggested that women showed similar changes in aBMD for different structural and biological reasons: women with narrow femoral necks showed smaller changes in BMC but greater increases in bone area compared to women with wide femoral necks who showed greater losses in BMC but without large compensatory increases in bone area. This finding is opposite to expectations that periosteal expansion acts to mechanically offset bone loss. Thus, changes in femoral neck structure and mass during menopause vary widely among women and are predicted by baseline external bone size but not aBMD. How these different structural and mass changes affect individual strengthâ decline trajectories remains to be determined. © 2017 American Society for Bone and Mineral Research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137625/1/jbmr3082.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137625/2/jbmr3082_am.pd