Fluctuation-Dissipation Theorem in Nonequilibrium Steady States

In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy}. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy}. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.Comment: 6 pages; EPL, in pres

Traveling-wave tube reliability estimates, life tests, and space flight experience

Infant mortality, useful life, and wearout phase of twt life are considered. The performance of existing developmental tubes, flight experience, and sequential hardware testing are evaluated. The reliability history of twt's in space applications is documented by considering: (1) the generic parts of the tube in light of the manner in which their design and operation affect the ultimate reliability of the device, (2) the flight experience of medium power tubes, and (3) the available life test data for existing space-qualified twt's in addition to those of high power devices

Half Cycle Pulse Train Induced State Redistribution of Rydberg Atoms

Population transfer between low lying Rydberg states independent of the initial state is realized using a train of half-cycle pulses with pulse durations much less than the classical orbit period. We demonstrate experimentally the transfer of population from initial states around n=50 down to n<40 as well as up to the continuum. The measured population transfer matches well to a model of the process for 1D atoms.Comment: V2: discussion extended, version accepted for publication in Physical Review

Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations

In three spatial dimensions, we study the Cauchy problem for the wave equation −∂[superscript 2][subscript t]Ψ + (1+Ψ)[superscript P] ΔΨ=0 for P∈{1,2}. We exhibit a form of stable Tricomi-type degeneracy formation that has not previously been studied in more than one spatial dimension. Specifically, using only energy methods and ODE techniques, we exhibit an open set of data such that Ψ is initially near 0, while 1+Ψ vanishes in finite time. In fact, generic data, when appropriately rescaled, lead to this phenomenon. The solution remains regular in the following sense: there is a high-order L[superscript 2]-type energy, featuring degenerate weights only at the top-order, that remains bounded. When P = 1, we show that any C[superscript 1] extension of Ψ to the future of a point where 1 + Ψ = 0 must exit the regime of hyperbolicity. Moreover, the Kretschmann scalar of the Lorentzian metric corresponding to the wave equation blows up at those points. Thus, our results show that curvature blowup does not always coincide with singularity formation in the solution variable. Similar phenomena occur when P = 2, where the vanishing of 1 + Ψ corresponds to the failure of strict hyperbolicity, although the equation is hyperbolic at all values of Ψ. The data are compactly supported and are allowed to be large or small as measured by an unweighted Sobolev norm. However, we assume that initially the spatial derivatives of Ψ are nonlinearly small relative to |∂[subscript t]Ψ|, which allows us to treat the equation as a perturbation of the ODE (d[superscript 2]/dt[superscript 2])Ψ = 0. We show that for appropriate data, ∂tΨ remains quantitatively negative, which simultaneously drives the degeneracy formation and yields a favorable spacetime integral in the energy estimates that is crucial for controlling some top-order error terms. Our result complements those of Alinhac and Lindblad, who showed that if the data are small as measured by a Sobolev norm with radial weights, then the solution is global. Keywords: degenerate hyperbolic; strictly hyperbolic; Tricomi equation; weakly hyperbolicNational Science Foundation (U.S.) (Grant DMS-1162211)National Science Foundation (U.S.) (Grant DMS-1454419

Spectral deferred corrections with fast-wave slow-wave splitting

The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves ("fast-wave slow-wave problem"). We show that for a scalar test problem with two imaginary eigenvalues iλ_fast, iλ_slow, having Δt(|λ_fast|+|λ_slow|)<1 is sufficient for the fast-wave slow-wave SDC (FWSW-SDC) iteration to converge and that in the limit of infinitely fast waves the convergence rate of the non-split version is retained. Stability function and discrete dispersion relation are derived and show that the method is stable for essentially arbitrary fast-wave CFL numbers as long as the slow dynamics are resolved. The method causes little numerical diffusion and its semi-discrete phase speed is accurate also for large wave number modes. Performance is studied for an acoustic-advection problem and for the linearised Boussinesq equations, describing compressible, stratified flow. FWSW-SDC is compared to a diagonally implicit Runge-Kutta (DIRK) and IMEX Runge-Kutta (IMEX) method and found to be competitive in terms of both accuracy and cost

The SiC problem: astronomical and meteoritic evidence

Pre-solar grains of silicon carbide found in meteorites and interpreted as having had an origin around carbon stars from their isotopic composition, have all been found to be of the beta-SiC polytype. Yet to date fits to the 11.3 microns SiC emission band of carbon stars had been obtained only for alpha-SiC grains. We present thin film infrared (IR) absorption spectra measured in a diamond anvil cell for both the alpha- and beta- polymorphs of synthetic SiC and compare the results with previously published spectra taken using the KBr matrix method. We find that our thin film spectra have positions nearly identical to those obtained previously from finely ground samples in KBr. Hence, we show that this discrepancy has arisen from inappropriate `KBr corrections' having been made to laboratory spectra of SiC particles dispersed in KBr matrices. We re-fit a sample of carbon star mid-IR spectra, using laboratory data with no KBr correction applied, and show that beta-SiC grains fit the observations, while alpha-SiC grains do not. The discrepancy between meteoritic and astronomical identifications of the SiC-type is therefore removed. This work shows that the diamond anvil cell thin film method can be used to produce mineral spectra applicable to cosmic environments without further manipulation.Comment: to be published in Astrophysical Journal Letter 4 pages, 3 figure

The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1+3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p=c[superscript 2]ρ,0 < c[superscript 2] < 1/3, the background metric + fluid solutions are globally future-stable under small irrotational perturbations of their initial data. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,∞)XT[superscript 3], are future causally geodesically complete. Our analysis is based on a combination of energy estimates and pointwise decay estimates for quasilinear wave equations featuring dissipative inhomogeneous terms. Our main new contribution is showing that when 0 < c[superscript 2] < 1/3, exponential spacetime expansion is strong enough to suppress the formation of fluid shocks. This contrasts against a well-known result of Christodoulou, who showed that in Minkowski spacetime, the corresponding constant-state irrotational fluid solutions are unstable

Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of view. We find that a variety of transient fluctuation theorems could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes

The Curious Conundrum Regarding Sulfur Abundances In Planetary Nebulae

Sulfur abundances derived from optical emission line measurements and ionization correction factors in planetary nebulae are systematically lower than expected for the objects' metallicities. We have carefully considered a large range of explanations for this "sulfur anomaly", including: (1) correlations between the size of the sulfur deficit and numerous nebular and central star properties; (2) ionization correction factors which under-correct for unobserved ions; (3) effects of dielectronic recombination on the sulfur ionization balance; (4) sequestering of S into dust and/or molecules; and (5) excessive destruction of S or production of O by AGB stars. It appears that all but the second scenario can be ruled out. However, we find evidence that the sulfur deficit is generally reduced but not eliminated when S^+3 abundances determined directly from IR measurements are used in place of the customary sulfur ionization correction factor. We tentatively conclude that the sulfur anomaly is caused by the inability of commonly used ICFs to properly correct for populations of ionization stages higher than S^+2.Comment: 40 pages, 14 figures, 3 tables. Accepted for publication in the Astrophysical Journa