The stochastic dynamics of nanoscale mechanical oscillators immersed in a viscous fluid

The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in experiment. We use this approach to investigate the fluid coupled motion of single and multiple cantilevers with experimentally motivated geometries.Comment: 5 pages, 5 figure

Equation of state for hard sphere fluids with and without Kac tails

In this note, we propose a simple derivation of the one dimensional hard rod equation of state, with and without a Kac tail (appended long range and weak potential). The case of hard spheres in higher dimension is also addressed and it is shown there that our arguments --which avoid any mathematical complication-- allow to recover the virial form of the equation of state in a direct way.Comment: pedagogical pape

Fluctuation-dissipation ratios in the dynamics of self-assembly

We consider two seemingly very different self-assembly processes: formation of viral capsids, and crystallization of sticky discs. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long term fate of the system, based on the early stages of assembly.Comment: 8 pages, 6 figure

Unveiling Sources of Heating in the Vicinity of the Orion BN/KL Hot Core as Traced by Highly Excited Inversion Transitions of Ammonia

Using the Expanded Very Large Array, we have mapped the vicinity of the Orion BN/KL Hot Core with sub-arcsecond angular resolution in seven metastable inversion transitions of ammonia: (J,K)=(6,6) to (12,12). This emission comes from levels up to 1500 K above the ground state, enabling identification of source(s) responsible for heating the region. We used this multi-transition dataset to produce images of the rotational/kinetic temperature and the column density of ammonia for ortho and para species separately and on a position-by-position basis. We find rotational temperature and column density in the range 160-490 K and (1-4)x10^17 cm^-2, respectively. Our spatially-resolved images show that the highest (column) density and hottest gas is found in a northeast-southwest elongated ridge to the southeast of Source I. We have also measured the ortho-para ratio of ammonia, estimated to vary in the range 0.9-1.6. Enhancement of ortho with respect to para and the offset of hot ammonia emission peaks from known (proto)stellar sources provide evidence that the ammonia molecules have been released from dust grains into the gas-phase through the passage of shocks and not by stellar radiation. We propose that the combined effect of Source I's proper motion and its low-velocity outflow impinging on a pre-existing dense medium is responsible for the excitation of ammonia and the Orion Hot Core. Finally, we found for the first time evidence of a slow (5 km/s) and compact (1000 AU) outflow towards IRc7.Comment: To appear in Astrophysical Journal Letters Special Issue on the EVLA. 8 pages, 4 figure

Modal Test of the NASA Mobile Launcher at Kennedy Space Center

The NASA Mobile Launcher (ML), located at Kennedy Space Center (KSC), has recently been modified to support the launch of the new NASA Space Launch System (SLS). The ML is a massive structureconsisting of a 345-foot tall tower attached to a two-story base, weighing approximately 10.5 million poundsthat will secure the SLS vehicle as it rolls to the launch pad on a Crawler Transporter, as well as provide a launch platform at the pad. The ML will also provide the boundary condition for an upcoming SLS Integrated Modal Test (IMT). To help correlate the ML math models prior to this modal test, and allow focus to remain on updating SLS vehicle models during the IMT, a ML-only experimental modal test was performed in June 2019. Excitation of the tower and platform was provided by five uniquely-designed test fixtures, each enclosing a hydraulic shaker, capable of exerting thousands of pounds of force into the structure. For modes not that were not sufficiently excited by the test fixture shakers, a specially-designed mobile drop tower provided impact excitation at additional locations of interest. The response of the ML was measured with a total of 361 accelerometers. Following the random vibration, sine sweep vibration, and modal impact testing, frequency response functions were calculated and modes were extracted for three different configurations of the ML in 0 Hz to 12 Hz frequency range. This paper will provide a case study in performing modal tests on large structures by discussing the Mobile Launcher, the test strategy, an overview of the test results, and recommendations for meeting a tight test schedule for a large-scale modal test

Thermodynamics of Quantum Jump Trajectories

We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments by exploiting the analogy between large-deviation and free-energy functions. This approach is particularly useful for uncovering properties of rare dissipative trajectories. We also prove, via an explicit quantum mapping, that rare trajectories of one system can be realized as typical trajectories of an alternative system.Comment: 5 pages, 3 figure

Entropy and Temperature of a Static Granular Assembly

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics, which is founded on the principle of conservation of energy, provides this framework. Grains, however, are small but macroscopic objects whose interactions are dissipative since energy can be lost through excitations of the internal degrees of freedom. In this work, we construct a statistical framework for static, mechanically stable packings of grains, which parallels that of equilibrium statistical mechanics but with conservation of energy replaced by the conservation of a function related to the mechanical stress tensor. Our analysis demonstrates the existence of a state function that has all the attributes of entropy. In particular, maximizing this state function leads to a well-defined granular temperature for these systems. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks. Our demonstration that a statistical ensemble can be constructed through the identification of conserved quantities other than energy is a new approach that is expected to open up avenues for statistical descriptions of other non-equilibrium systems.Comment: 5 pages, 4 figure

Entropy and density of states from isoenergetic nonequilibrium processes

Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)], which can be seen as a ``fast-switching'' version of the adiabatic switching method for computing entropies [M. Watanabe, W. P. Reinhardt, Phys. Rev. Lett. 65, 3301 (1990)]. The second is a thermodynamic integration formula analogous to a well-known expression for free energies, and follows after taking the quasistatic limit of the first. Both identities can be conveniently used in conjunction with a scaling relation (herein derived) that allows one to extrapolate measurements taken at a single energy to a wide range of energy values. Practical aspects of these identities in the context of numerical simulations are discussed.Comment: 5 pages, no figure