Orders Of Magnitude In Frequency Research Articles

Delays and Oscillations in Networks of Spiking Neurons: A Two-Timescale Analysis

Oscillations are a ubiquitous feature of many neural systems, spanning many orders of magnitude in frequency. One of the most prominent oscillatory patterns, with possible functional implications, is that occurring in the mammalian thalamocortical system during sleep. This system is characterized by relatively long delays (reaching up to 40 msec) and gives rise to low-frequency oscillatory waves. Motivated by these phenomena, we study networks of excitatory and inhibitory integrate-and-fire neurons within a Fokker-Planck delay partial differential equation formalism and establish explicit conditions for the emergence of oscillatory solutions, and for the amplitude and period of the ensuing oscillations, for relatively large values of the delays. When a two-timescale analysis is employed, the full partial differential equation is replaced in this limit by a discrete time iterative map, leading to a relatively simple dynamic interpretation. This asymptotic result is shown numerically to hold, to a good approximation, over a wide range of parameter values, leading to an accurate characterization of the behavior in terms of the underlying physical parameters. Our results provide a simple mechanistic explanation for one type of slow oscillation based on delayed inhibition, which may play an important role in the slow spindle oscillations occurring during sleep. Moreover, they are consistent with experimental findings related to human motor behavior with visual feedback.

WMAP haze: Directly observing dark matter?

In this paper we show that dark matter in the form of dense matter/antimatter nuggets could provide a natural and unified explanation for several distinct bands of diffuse radiation from the core of the Galaxy spanning over 12 orders of magnitude in frequency. We fix all of the phenomenological properties of this model by matching to x-ray observations in the keV band, and then calculate the unambiguously predicted thermal emission in the microwave band, at frequencies smaller by 10 orders of magnitude. Remarkably, the intensity and spectrum of the emitted thermal radiation are consistent with--and could entirely explain--the so-called "WMAP haze": a diffuse microwave excess observed from the core of our Galaxy by the Wilkinson Microwave Anisotropy Probe (WMAP). This provides another strong constraint of our proposal, and a remarkable nontrivial validation. If correct, our proposal identifies the nature of the dark matter, explains baryogenesis, and provides a means to directly probe the matter distribution in our Galaxy by analyzing several different types of diffuse emissions.

Thermoreversible Supramacromolecular Ion Gels via Hydrogen Bonding

We report the thermoreversible viscoelastic properties of a supramolecular ion gel. Two building blocks were used to form “supramacromolecules”. An ABA triblock copolymer (Mn = 50 000, poly(2-vinylpyridine)-b-poly(ethyl acrylate)-b-poly(2-vinylpyridine)) (P2VP−PEA−P2VP), with a mole ratio of 0.1/0.8/0.1 as a telechelic polymer, and a poly(4-hydroxystyrene) (PHS) homopolymer, with Mn = 6600 as a connector, form a physical gel via hydrogen bonding between P2VP and PHS. The thermally stable, hydrophobic ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMITFSI) provided a good solvent medium for PEA from room temperature up to at least 160 °C. A solution containing 10 wt % P2VP−PEA−P2VP and 4% PHS was a liquid at elevated temperatures but on cooling formed a network at 141.5 °C. Dynamic shear moduli obtained as a function of frequency at various temperatures from 30 to 160 °C could be superposed to form excellent master curves, with a distinct plateau modulus extending over more than 11 orders of magnitude in frequency. The longest relaxation time inferred from the time−temperature superposition shift factors showed a similar 11 order of magnitude increase on cooling. This remarkable temperature sensitivity of the supramacromolecular ion gel is attributed to the formation of multiple hydrogen bonds between a given P2VP block and PHS cross-linker. A hydrogen bond energy of 13 kJ/mol was estimated from temperature-dependent FTIR measurements, and a straightforward analysis yielded an estimate of the number of hydrogen bonds per P2VP block as a function of temperature. This system is distinct from other supramolecular hydrogen-bonded polymers, and from hydrophobically modified associating polymers, in that below the gelation temperature the number of physical cross-links is independent of temperature, but the strength of each association, namely, the number of active hydrogen bonds within a particular cross-link site, increases strongly on cooling.

On the computation and contribution of conductivity in molecular ionic liquids

In this study we present the results of the molecular dynamics simulation of the ionic liquids: 1-butyl-3-methyl-imidazolium tetrafluoroborate and trifluoromethylacetate as well as 1-ethyl-3-methyl-imidazolium dicyanamide. Ionic liquids are characterized by both a molecular dipole moment and a net charge. Thus, in contrast to a solution of simple ions in a (non-) polar solvent, rotational and translational effects influence the very same molecule. This study works out the theoretical framework necessary to compute the conductivity spectrum and its low frequency limit of ionic liquids. Merging these computed conductivity spectra with previous simulation results on the dielectric spectra of ionic liquids yields the spectrum of the generalized dielectric constant, which may be compared to experiments. This spectrum was calculated for the three ionic liquids over six orders of magnitude in frequency ranging from 10 MHz to 50 THz. The role of rotation and translation and their coupling term on the generalized dielectric constant is discussed in detail with a special emphasis on the zero-frequency limit. Thereby, the frequency dependence of the cross correlation between the collective rotational dipole moment and the current is discussed.

Tracing the Jet Contribution to the Mid‐IR over the 2005 Outburst of GRO J1655−40 via Broadband Spectral Modeling

We present new results from a multiwavelength (radio/infrared/optical/X-ray) study of the black hole X-ray binary GRO J1655-40 during its 2005 outburst. We detected, for the first time, mid-infrared emission at 24 μm from the compact jet of a black hole X-ray binary during its hard state, when the source shows emission from a radio compact jet, as well as a strong nonthermal hard X-ray component. These detections strongly constrain the optically thick part of the synchrotron spectrum of the compact jet, which is consistent with it being flat over 4 orders of magnitude in frequency. Moreover, using this unprecedented coverage, and especially thanks to the new Spitzer observations, we can test broadband disk and jet models during the hard state. Two of the hard-state broadband spectra are reasonably well fitted using a jet model with parameters that overall are similar to those previously found for Cyg X-1 and GX 339-4. Differences are also present; most notably, the jet power in GRO J1655-40 appears to be a factor of at least ~3-5 higher (depending on the distance) than those of Cyg X-1 and GX 339-4 at comparable disk luminosities. Furthermore, a few discrepancies between the model and the data, previously not found for the other two black hole systems for which there was no mid-IR/IR and optical coverage, are evident, and will help to constrain and refine theoretical models.

Interpretations for Low‐ and High‐Frequency QPO Correlations of X‐Ray Sources among White Dwarfs, Neutron Stars, and Black Holes

ABSTRACTAn empirical linear relation is found to exist between the high and low frequencies (νhigh, νlow) of quasi‐periodic oscillations (QPOs) for black hole candidates (BHCs), neutron stars (NSs), and white dwarfs (WDs) in binary systems, spanning 5 orders of magnitude in frequency. For the NS Z (atoll) sources, νhigh and νlow are identified as the lower kHz QPO frequency and horizontal‐branch oscillation (HBO) frequency νHBO (broad noise components); for the BHCs and low‐luminosity NSs, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the “dwarf nova oscillations” (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes νhigh to the Alfvén wave oscillation frequency at a preferred radius, and νlow to the same mechanism at another radius. We can then obtain νlow = 0.08νhigh and the relation between the upper kHz QPO frequency ν2 and the HBO frequency, νHBO≃(56 Hz)(ν2/kHz)2, which are in accordance with the observed empirical relations. Furthermore, some implications of the model are discussed, including why QPO frequencies of WDs and NSs span 5 orders of magnitude.

Timescale of variation and the size of the accretion disc in active galactic nuclei

This paper sets out to measure the timescale of quasar variability with a view to new understanding of the size of accretion discs in active galactic nuclei. Previous attempts to measure such timescales have been based on sparsely sampled data covering small ranges of time. Here we combine data from two large scale monitoring programmes to obtain Fourier power spectra of light curves covering nearly three orders of magnitude in frequency in blue and red passbands. If the variations are interpreted as due to gravitational microlensing, then timescale measurements in the observer's frame imply a minimum mass for the microlensing bodies of around $0.4~M_{\odot}$. On the assumption that the variations are intrinsic to the quasars, a correction must be made for time dilation. In this case the power spectrum shows a break corresponding to a timescale of about 11 years. This timescale is used to measure the size of the accretion disc, which is found to be about 10 -2 pc or 10 light days, in agreement with limits set by self-gravitation and coincident with the broad line region of the active galactic nucleus. It is suggested that the broad line region may be associated with the break up of the outer part of the accretion disc.

Asymptotic description of schematic models for CKN

The fits of 0.4Ca(NO3)20.6 K(NO3) (CKN) by schematic mode-coupling models [V. Krakoviack, C. Alba-Simionesco, J. Chem. Phys. 117 (2002), 2161] are analyzed by asymptotic expansions. The validity of both the power-law and the Cole–Cole-peak solutions for the critical spectrum are investigated. It is found that the critical spectrum derived from the fits is described by both expansions equally well when both expansions are carried out up to next-to-leading order. The expansions up to this order describe the data for 373K over two orders of magnitude in frequency. In this regime an effective power-law ωa can be identified where the observed exponent a is smaller than its calculated value by about 15%; this finding can be explained by corrections to the leading-order terms in the asymptotic expansions. For higher temperatures, even smaller effective exponents are caused by a crossover to the alpha-peak spectrum.

Direct detection of the inflationary gravitational-wave background

Inflation generically predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO) or Japan's Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO), both currently under study. Here we investigate the detectability of the inflationary gravitational-wave background at BBO/DECIGO frequencies. To do so, we survey a range of slow-roll inflationary models consistent with constraints from the CMB and large-scale structure (LSS). We go beyond the usual assumption of power-law power spectra, which may break down given the 16 orders of magnitude in frequency between the CMB and direct detection, and solve instead the inflationary dynamics for four classes of inflaton potentials. Direct detection is possible in a variety of inflationary models, although probably not in any in which the gravitational-wave signal does not appear in the CMB polarization. However, direct detection by BBO/DECIGO can help discriminate between inflationary models that have the same slow-roll parameters at CMB/LSS scales.

Neuronal oscillations in cortical networks.

Clocks tick, bridges and skyscrapers vibrate, neuronal networks oscillate. Are neuronal oscillations an inevitable by-product, similar to bridge vibrations, or an essential part of the brain's design? Mammalian cortical neurons form behavior-dependent oscillating networks of various sizes, which span five orders of magnitude in frequency. These oscillations are phylogenetically preserved, suggesting that they are functionally relevant. Recent findings indicate that network oscillations bias input selection, temporally link neurons into assemblies, and facilitate synaptic plasticity, mechanisms that cooperatively support temporal representation and long-term consolidation of information.

Linear viscoelastic behavior of densely grafted poly(chloroethyl vinyl ether)-g-polystyrene combs in the melt

We have measured the linear viscoelastic behavior in the melt of two densely grafted poly(chloroethyl vinyl ether)-g-polystyrene comb polymers. Both samples have a backbone of approximately 800 ethyl vinyl ether monomers and the fractions of grafted backbone monomers are 98% and 10%, respectively. The viscoelastic behavior shows remarkable features. The comb polymer with the highest grafting density shows a power law behavior over five orders of magnitude in frequency. The power law can be understood through a “Rouse-like” motion of the entire chains with an apparent friction coefficient coming from the fast Rouse dynamics of the short grafts. Alternatively, the same behavior can be described as the signature of a “fluctuating” physical gel. The less densely grafted comb polymer has a more complex behavior.

The Properties of Small Magnetic Regions on the Solar Surface and the Implications for the Solar Dynamo(s)

We find that bipolar active regions that emerge onto the Sun's surface are part of a smoothly decreasing frequency distribution that spans almost 4 orders of magnitude in flux and 8 orders of magnitude in frequency. Distributions of emergence latitude and dipole orientation narrow from nearly uniform for the smallest observed ephemeral regions (~5 × 1018 Mx) up to narrowly distributed about the mean for the largest active regions (close to 1022 Mx), while the emergence frequency increases smoothly and rapidly with decreasing flux. At the low end of the flux spectrum, the cycle variation in emergence frequency is at most a factor of 1.5, in antiphase with the cycle variation of close to an order of magnitude for the large active regions. We discuss a scenario in which the ephemeral regions with fluxes below ~30 × 1018 Mx have their origin in a turbulent dynamo, largely independent of the global sunspot cycle. Our empirical findings are based on a combination of previously published work on active regions and large ephemeral regions, complemented here with an analysis of the photospheric magnetic field outside active regions, as observed in SOHO/MDI full-disk magnetograms taken from the most recent sunspot minimum in 1996 to about 1 yr after sunspot maximum in 2001. We find that the spectrum of the emerging bipoles with fluxes (6-30) × 1018 Mx can be approximated throughout this period by a fixed exponential distribution with an e-folding scale of (5.3 ± 0.1) × 1018 Mx. We confirm that the ephemeral regions are an important source of flux for the quiet magnetic network, in particular for the smallest scales; the larger scale patterns are dominated by flux dispersing from decaying active regions. As the variation of these two sources is nearly in antiphase, the flux contained in the quiet-Sun network shows little overall variation: the flux spectrum and the total absolute flux for network concentrations with fluxes 20 × 1018 Mx are essentially independent of cycle phase. For network concentrations with fluxes 30 × 1018 Mx, mostly found in regions populated substantially by decayed active regions, the network flux distribution approaches an exponential for which the e-folding scale increases with sunspot activity from ~20 × 1018 Mx to ~33 × 1018 Mx, as the total flux in this component varies in phase with the sunspot cycle. A comparison of the flux-emergence rate with the network flux implies an overall mean replacement time for flux in quiet Sun of 8-19 hr.

Power spectrum of sea level change over fifteen decades of frequency

The power spectrum of relative sea level change has been estimated over more than 15 orders of magnitude in frequency, from a frequency of 1/(591 Ma) to a frequency of 1/(5 s). Although there are still regions of the spectrum where data sampling and duration do not allow the power to be calculated, most notably between periods of 100–1000 years, the general shape of the spectrum is that in which the power depends on the square of the reciprocal frequency, apart from periods between 1 and 100 years where the power spectrum falls off less steeply with increasing frequency. A spectrum in which power depends on reciprocal frequency squared is the same spectrum as that calculated from a random walk signal of finite length. There are some causes that have defined frequencies, such as those associated with tides and the Milankovitch cycles of the ice ages, but there is also a continuum of relative sea level change that requires other causes. The implications of this are discussed in the light of global change and heating of the lithosphere from the bottom.

Correlation of the Quasi‐Periodic Oscillation Frequencies of White Dwarf, Neutron Star, and Black Hole Binaries

Using data obtained in 1994 June/July with the Extreme Ultraviolet Explorer deep survey photometer and in 2001 January with the Chandra X-ray Observatory Low Energy Transmission Grating Spectrograph, we investigate the extreme-ultraviolet (EUV) and soft X-ray oscillations of the dwarf nova SS Cyg in outburst. We find quasi-periodic oscillations (QPOs) at nu_0 ~ 0.012 Hz and nu_1 ~ 0.13 Hz in the EUV flux and at nu_0 ~ 0.0090 Hz, nu_1 ~ 0.11 Hz, and possibly nu_2 ~ nu_0 + nu_1 ~ 0.12 Hz in the soft X-ray flux. These data, combined with the optical data of Woudt & Warner for VW Hyi, extend the Psaltis, Belloni, & van der Klis nu_high-nu_low correlation for neutron star and black hole low-mass X-ray binaries (LMXBs) nearly two orders of magnitude in frequency, with nu_low ~ 0.08 nu_high. This correlation identifies the high-frequency quasi-coherent oscillations (so-called ``dwarf nova oscillations'') of cataclysmic variables (CVs) with the kilohertz QPOs of LMXBs, and the low-frequency QPOs of CVs with the horizontal branch oscillations (or the broad noise component identified as such) of LMXBs. Assuming that the same mechanisms produce the QPOs in white dwarf, neutron star, and black hole binaries, we find that the data exclude the relativistic precession model and the magnetospheric and sonic-point beat-frequency models (as well as any model requiring the presence or absence of a stellar surface or magnetic field); more promising are models that interpret QPOs as manifestations of disk accretion onto any low-magnetic field compact object.

Step response analysis in DSC — a fast way to generate heat capacity spectra

A new method of step response analysis in DSC was developed which allows the fast generation of heat capacity spectra. In common temperature modulated calorimetry, like 3ω-method, AC-calorimetry and temperature modulated differential scanning calorimetry (TMDSC), periodic perturbations are used to get dynamic heat capacity. In contrary, the proposed method uses a single step in program temperature followed by an isothermal segment to obtain the spectrum of heat capacity. To follow system evolution with time or temperature, one can repeat the temperature step, like in StepScan-DSC™ (PerkinElmer Instruments), several times also in a non-periodic manner. Measured heat flow rate is evaluated in time domain. With this method, it is possible to cover more than two orders of magnitude in frequency in a single measurement. This allows a dramatic shortening of the measuring time compared to TMDSC. A linearity check and the comparison with TMDSC results are presented. Complete data analysis is performed by a software available for download from our website.

Spectral shape of relaxations in silica glass

Precise low-frequency light scattering experiments on silica glass are presented, covering a broad temperature and frequency range ( 9 GHz<nu<2 THz). The spectra show a power-law low-frequency wing of the relaxational part of the spectrum with an exponent alpha proportional to temperature in the range 30<T<200 K. A comparison of our results with those from acoustic attenuation experiments performed at different frequencies shows that this power-law behavior rather well describes relaxations in silica over 9 orders of magnitude in frequency. These findings can be explained by a model of thermally activated transitions in double well potentials.

Correlations in Quasi‐periodic Oscillation and Noise Frequencies among Neutron Star and Black Hole X‐Ray Binaries

We study systematically the ^0.1¨1200 Hz quasi-periodic oscillations (QPOs) and broad noise com- ponents observed in the power spectra of nonpulsing neutron star and black hole low-mass X-ray binaries. We show that among these components we can identify two, occurring over a wide range of source types and luminosities, whose frequencies follow a tight correlation. The variability components involved in this correlation include neutron star kilohertz QPOs and horizontal-branch oscillations, as well as black hole QPOs and noise components. Our results suggest that the same types of variability may occur in both neutron star and black hole systems over 3 orders of magnitude in frequency and with coherences that vary widely but systematically. Con—rmation of this hypothesis will strongly con- strain theoretical models of these phenomena and provide additional clues to understanding their nature. Subject headings: accretion, accretion disksblack hole physicsstars: neutron ¨ stars: oscillationsX-rays: stars

Fluctuations with a 1/f α spectrum in film boiling

1/f and 1/f2 noise were observed experimentally in film boiling of water on vertically oriented platinum heater. Fluctuations with a 1/f α spectrum were observed in a wide range of controlling parameters and seen over five orders of magnitude in frequency. It was noted that the process investigated is similar to the phenomenon of self-organized criticality.

30 years of multi-wavelength observations of 3C 273

We present a wide multi-wavelength database of most observations of the quasar 3C 273 obtained during the last 30 years. This database is the most complete set of observations available for an active galactic nucleus (AGN). It contains nearly 20'000 observations grouped together into 70 light curves covering 16 orders of magnitude in frequency from the radio to the gamma-ray domain. The database is constituted of many previously unpublished observations and of most publicly available data gathered in the literature and on the World Wide Web (WWW). It is complete to the best of our knowledge, except in the optical (UBV) domain where we chose not to add all observations from the literature. In addition to the photometric data, we present the spectra of 3C 273 obtained by the International Ultraviolet Explorer (IUE) satellite. In the X-ray domain, we used the spectral fit parameters from the literature to construct the light curves. Apart from describing the data, we show the most representative light curves and the average spectrum of 3C 273. The database is available on the WWW in a homogeneous and clear form and we wish to update it regularly by adding new observations.

Influence of disorder on the vortex-lattice melting in twinned oxygen-deficient ortho-IIYBa2Cu3Oy(y≈6.6)

We investigated with ac susceptibility the mixed state of twinned, deoxygenated single crystals and highly $c$-axis-oriented melt-textured samples of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ with oxygen stoichometry corresponding to that of the orthorhombic II phase. In the single crystal we found, below ${H}^{*}\ensuremath{\approx}700$ Oe and over almost four orders of magnitude in frequency, a frequency-independent ``irreversibility line'' (IL). Complementry dc magnetization measurements seem to disregard an IL arising from geometric effects when $H\ensuremath{\Vert}c$, and they suggest a possible meltinglike transition of the flux-line lattice below ${H}^{*}$. The reduced value of ${H}^{*}$ is associated with the increased anisotropy induced by the oxygen depletion, and an upper limit of the anisotropy parameter is estimated as ${\ensuremath{\gamma}}_{\mathrm{max}}\ensuremath{\approx}147$. However, in the twinned melt-textured sample having a major grade of disorder due to the presence of micrometric nonsuperconducting precipitates of ${\mathrm{Y}}_{2}{\mathrm{BaCuO}}_{5}$, the IL is frequency dependent for all applied magnetic fields, suggesting a cancellation of ${H}^{*}$ in the sufficiently disordered specimen.