On the anomalous thermal conductivity of one-dimensional lattices

The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A possible explanation in the framework of linear-response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes. Finally, the results of dynamical simulations are compared with the predictions of mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

Reverse the Curse: Colonialist Legacies of the Magic Poem

This dissertation investigates the conceptual relationships between poetry, magic, and race and their effects on both intellectual and creative practices from modernism through the post-war era. In doing so, this study works cross-disciplinarily, tracing early anthropological and sociological characterizations of primitive religion in connection to early-to-mid-twentieth-century literary study and writing. In working across disciplines at this particularly fungible moment in the history of the academy, this dissertation attempts to understand how the concurrent colonial global context effects the production and organization of knowledge just prior to and during modernism. It ultimately seeks to de-colonize literary thinking about poetry by performing a racial critique of the role of magical thinking in its generic conception and production. The first chapter establishes the intellectual history of the dissertation’s key problem, the presence of primitivism throughout modernist and post-modernish approaches to poetry and the desire for this poetry to offer reparation; examines the ethnographic texts, especially Marcel Mauss’s General Theory of Magic, that relate poetic language to the language of magic ritual and animistic belief systems; considers how these foundational beliefs continued to influence modernist critics like Theodor Adorno and C.L.R. James, and how certain poets and critics attempt to subvert these intellectual trends that associate blackness with magic and magic with poetry; and lastly questions the ethical implications of assuming that poetry’s “magic” could cure socio-cultural loss. The second and third chapters further develop and test the dissertation’s argument that regardless of poets’ intentions, magic operates within their understanding of poetic function, and that these understandings stem from racist, colonialist understandings of primitive space, time, and culture, while simultaneously attempting to understand their works’ attitude toward poetic reparation. In the second chapter, I examine Gertrude Stein’s 1932 Stanzas in Meditation in an attempt to understand the text’s relationship to concepts of magical language, and its trance-like, reparative effect on readers, an effect complicated by its appropriation of primitivist concepts of time. In the final chapter, I turn to Amiri Baraka’s 1969 compilation Black Magic to explore this work’s relationship to its titular “magic.” I ultimately demonstrate how Baraka’s work re-theorizes a kind of poetic spirituality that eschews white capitalist magic and offers a materialist, pragmatic poetics for surviving racism and strengthening Black consciousness. In concluding, I look to the contemporary moment and claim that the current upswing in the poetry community’s interest in the occult serves as further evidence for one, how the role of magic and poetry corresponds to a social desire for reparation, and, two, how the racialized thinking at stake in the invocation of magic in poetry continues to merit critical and popular examination

Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is $L\times L\times 2L$, and the heat is made to flow in the $2L$ direction the Nose-Hoover method. Although a linear temperature profile is realized, the ratio of enerfy flux to temperature gradient shows logarithmic divergence with $L$. The autocorrelation function of energy flux $C(t)$ is observed to show power-law decay as $t^{-0.98\pm 0,25}$, which is slower than the decay in conventional momentum-cnserving three-dimensional systems ($t^{-3/2}$). Similar behavior is also observed in the four dimensional system.Comment: 4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan Letter

Asymptotic energy profile of a wavepacket in disordered chains

We investigate the long time behavior of a wavepacket initially localized at a single site $n_0$ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile $\bar{< e_n(t)>}$ averaged on time and disorder decays for large $|n-n_0|$ as a power law $\bar{}\approx C|n-n_0|^{-\eta}$ where $\eta=5/2$ and 3/2 for initial displacement and momentum excitations, respectively. The prefactor $C$ depends on the probability distribution of the harmonic coupling constants and diverges in the limit of weak disorder. As a consequence, the moments $< m_{\nu}(t)>$ of the energy distribution averaged with respect to disorder diverge in time as $t^{\beta(\nu)}$ for $\nu \geq 2$, where $\beta=\nu+1-\eta$ for $\nu>\eta-1$. Molecular dynamics simulations yield good agreement with these theoretical predictions. Therefore, in this system, the second moment of the wavepacket diverges as a function of time despite the wavepacket is not spreading. Thus, this only criteria often considered earlier as proving the spreading of a wave packet, cannot be considered as sufficient in any model. The anharmonic case is investigated numerically. It is found for intermediate disorder, that the tail of the energy profile becomes very close to those of the harmonic case. For weak and strong disorder, our results suggest that the crossover to the harmonic behavior occurs at much larger $|n-n_0|$ and larger time.Comment: To appear in Phys. Rev.

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other. The supratransmission regime occurs for driving frequencies above the upper band-edge and originates from direct moving discrete breather creation. We derive approximate analytical estimates of the supratransmission threshold, which are in excellent agreement with numerics. When analysing the long-time behavior, we discover that, below the supratransmission threshold, a conducting stationary state coexists with the insulating one. We explain the bistable nature of the energy flux in terms of the excitation of quasi-harmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.Comment: 8 pages, 9 figures. Phys. Rev. E (accepted

Anomalies, absence of local equilibrium and universality in 1-d particles systems

One dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the dependence of the behaviour of one dimensional, time reversal invariant, nonequilibrium systems on the parameters defining their microscopic dynamics. In particular, we consider chains of identical oscillators interacting via hard core elastic collisions and harmonic potentials, driven by boundary Nos\'e-Hoover thermostats. Their behaviour mirrors qualitatively that of stochastically driven systems, showing that anomalous properties are typical of physics in one dimension. Chaos, by itslef, does not lead to standard behaviour, since it does not guarantee local thermodynamic equilibrium. A linear relation is found between density fluctuations and temperature profiles. This link and the temporal asymmetry of fluctuations of the main observables are robust against modifications of thermostat parameters and against perturbations of the dynamics.Comment: 26 pages, 16 figures, revised text, two appendices adde

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

Ion Charge States in Halo CMEs: What can we Learn about the Explosion?

We describe a new modeling approach to develop a more quantitative understanding of the charge state distributions of the ions of various elements detected in situ during halo Coronal Mass Ejection (CME) events by the Advanced Composition Explorer (ACE) satellite. Using a model CME hydrodynamic evolution based on observations of CMEs propagating in the plane of the sky and on theoretical models, we integrate time dependent equations for the ionization balance of various elements to compare with ACE data. We find that plasma in the CME ``core'' typically requires further heating following filament eruption, with thermal energy input similar to the kinetic energy input. This extra heating is presumably the result of post eruptive reconnection. Plasma corresponding to the CME ``cavity'' is usually not further ionized, since whether heated or not, the low density gives freeze-in close the the Sun. The current analysis is limited by ambiguities in the underlying model CME evolution. Such methods are likely to reach their full potential when applied to data to be acquired by STEREO when at optimum separation. CME evolution observed with one spacecraft may be used to interpret CME charge states detected by the other.Comment: 20 pages, accepted by Ap

Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier

We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.Comment: 4 pages with figures included. Phys. Rev. Lett., to be published (Ref. [10] corrected