The Debye theory of solid-state heat capacities

“The Debye theory of solid-state heat capacities” gives a careful account of the Debye cut-off. We start by looking at a monatomic linear chain, leading to degrees of freedom and the equipartition of energy at the high-temperature (classical) limit. Reasonable approximations lead more naturally to the Born–von Karman model than to Debye, but Debye follows via a further reasonable step.

Random vibration analysis and modal energy characteristics of fiber-reinforced composite beams

In aerospace and automotive industries, structural designs are required to meet specific weight limits whilst maintaining strength and stiffness. The material of choice for such applications is fiber-reinforced composites because of their high strength-to-weight and stiffness-to-weight ratios. Composite materials used in these applications are often subjected to random dynamic loads and if the excitation sources are large enough, excessive vibration can lead to unwanted noise levels and fatigue failure. A commonly used design tool for modeling the vibration transmission and power flow in structures excited by random forces is statistical energy analysis. In order to incorporate fiber-reinforced composites within a statistical energy analysis methodology, a detailed understanding of how the modal energy levels vary when excited by a broadband random excitation source is needed. In this paper, analytical expressions are derived for the modal energy levels of a fiber-reinforced composite beam coupled in bending and torsion subjected to spatial white noise or the so-called rain-on-the-roof loading. It is shown that the modal energy levels of the fiber-reinforced composite beam are markedly nonuniform across the modal spectrum. This finding is in contrast with the well-known classical result that an isotropic beam subjected to the same type of excitation is characterized by a uniform modal energy spectrum, a result sometimes referred to as the equipartition of energy. The equipartition of energy forms the basis of statistical energy analysis and the results of this work indicate that fiber-reinforced composite beams cannot be reliably included into a conventional statistical energy analysis methodology. It is also shown that the mechanism responsible for the nonuniform modal energy distribution is related to the physical process by which power is transmitted across the boundaries. Simulations are also carried out to illustrate that the distribution characteristics of the modal energy are identical for a range of classical boundary conditions.

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling

We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 108 at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.

Maxwell: the rise of statistical mechanics

Maxwell produced two publications on the kinetic theory of gases in which he proposed his eponymous velocity distribution of velocities, his theory on the equipartition of energy, and finally his famed transport equations. In this work he surprisingly predicted that gas viscosity is independent of density and then confirmed this finding in experiments he conducted with his wife.

Radio view of a broad-line Type Ic supernova ASASSN-16fp

ABSTRACT We present extensive radio observations of a Type Ic supernova, ASASSN-16fp. Our data represent the lowest frequency observations of the supernova beyond 1000 d with a frequency range of 0.33–25 GHz and a temporal range of ∼8–1136 d post-explosion. The observations are best represented by a model of synchrotron emission from a shocked circumstellar shell initially suppressed by synchrotron self-absorption. Assuming equipartition of energy between relativistic particles and magnetic fields, we estimate the velocity and radius of the blast wave to be $v$ ∼ 0.15c and r ∼ 3.4 × 1015 cm, respectively, at t0 ∼ 8 d post-explosion. We infer the total internal energy of the radio-emitting material evolves as E ∼ 0.37 × 1047 (t/t0)0.65 erg. We determine the mass-loss rate of the progenitor star to be $\dot{M} \sim (0.4\!-\!3.2) \times 10^{-5}\, \mathrm{M}_{\odot }\, \rm yr^{-1}$ at various epochs post-explosion, consistent with the mass-loss rate of Galactic Wolf–Rayet stars. The radio light curves and spectra show a signature of density enhancement in the circumstellar medium at a radius of ∼1.10 × 1016 cm from the explosion centre.

Whistler instabilities from the interplay of electron anisotropies in space plasmas: a quasi-linear approach

ABSTRACT Recent statistical studies of observational data unveil relevant correlations between whistler fluctuations and the anisotropic electron populations present in space plasmas, e.g. solar wind and planetary magnetospheres. Locally, whistlers can be excited by two sources of free energy associated with anisotropic electrons, i.e. temperature anisotropies and beaming populations carrying the heat flux. However, these two sources of free energy and the resulting instabilities are usually studied independently preventing a realistic interpretation of their interplay. This paper presents the results of a parametric quasi-linear study of the whistler instability cumulatively driven by two counter-drifting electron populations and their anisotropic temperatures. By comparison to individual regimes dominated either by beaming population or by temperature anisotropy, in a transitory regime the instability becomes highly conditioned by the effects of both these two sources of free energy. Cumulative effects stimulate the instability and enhance the resulting fluctuations, which interact with electrons and stimulate their diffusion in velocity space, leading to a faster and deeper relaxation of the beaming velocity associated with a core heating in perpendicular direction and a thermalization of the beaming electrons. In particular, the relaxation of temperature anisotropy to quasi-stable states below the thresholds conditions predicted by linear theory may explain the observations showing the accumulation of these states near the isotropy and equipartition of energy.