A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Burst distribution of a linear code

In this note, the distribution of bursts is obtained, as defined by Chien and Teng, for a linear code and its coset.     

Effects of metal ion binding on an oncomodulin mutant containing a novel calcium-binding loop

The Ca²⁺-binding protein oncomodulin was altered by cassette mutagenesis of the CD site (CDOM33) with a sequence that was derived by a consensus method using over 250 known Ca²⁺-binding loop sequences. This mutant was studied using time-resolved and steady-state fluorescence from the Trp residue included at position 7 of the loop (position 57 of the protein sequence). The fluorescence characteristics of this species in the absence and presence of metal ions were compared to those of a tetradecapeptide containing the loop and the single Trp mutant of oncomodulin, Y57W. The fluorescence properties of CDOM33 were quite different from the peptide, both in the apo form and in response to metal binding. The consensus CD loop in CDOM33 exhibited the characteristics of a Ca²⁺/Mg²⁺ site in contrast to the Ca²⁺ specificity of the wild-type CD loop. The Trp analogue, 5-hydroxytryptophan (5HW), was incorporated into both oncomodulin mutants to produce Y75(5HW) and 5HW-CDOM33. Results showed that this intrinsic probe was relatively insensitive to structural changes in the mutants upon metal binding compared to Trp itself.     

The vertical plate in laminar free convection: Effects of leading and trailing edges and discontinuous temperature

Summary For laminar free-convection flow past a heated vertical plate of finite length, the local asymptotic flow structure is studied in regions where the boundary-layer equations do not provide a correct approximation at large Grashof numbers. The leading-edge region is shown to contribute a secondorder term to the integrated heat transfer. An integral form of the energy equation permits calculation of this correction in terms of the second-order boundary-layer solution away from the edge, without knowledge of the flow details near the edge, which can be obtained only by solution of the full Navier-Stokes equations. Near the trailing edge and near a jump in the prescribed plate temperature the longitudinal pressure gradient is found to be important in a thin sublayer adjacent to the plate, and the transverse pressure gradient is important in the remainder of the boundary layer, each for a distance along the plate which is slightly larger in order of magnitude than the boundary-layer thickness. At the trailing edge the sublayer problem is nonlinear and cannot be solved analytically, but it can be shown that the local correction to the total heat transfer is of slightly larger order of magnitude than the leading-edge correction. It is pointed out that the trailing-edge flow is identical in form to the flow near the edge of a rotating disc in a stationary fluid. The temperature-jump problem is linear and a solution is given which shows how the singularity in streamline slope predicted by the boundary-layer solution is removed.

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Zusammenfassung Bei laminarer natürlicher Strömung längs einer senkrecht stehenden endlichen geheizten Platte bei sehr grossen Grashof'schen Zahlen gibt es kleine Bereiche, bei denen die Grenzschichtgleichungen keine echte asymptotische Darstellung liefern. Im Vorderkantenbereich findet man ein Zusatzglied zweiter Ordnung für die gesamte Wärmeübertragung. Die Berechnung dieser Korrektur erfolgt durch eine Integralform der Energiegleichung, wobei nur die Lösung der Grenzschichtgleichung zweiter Ordnung fern von der Kante benützt wird, während die Kenntnis der Strömung in der Nähe der Kante nur durch eine Lösung der exakten Navier-Stokes'schen Gleichungen gefunden werden könnte. In der Nähe der Hinterkante und in der Nähe einer Diskontinuität der gegebenen Plattentemperatur wird das Längsdruckgefälle in einer dünnen Unterschicht wichtig; das Querdruckgefälle wird in dem restlichen Teil der Grenzschicht berücksichtigt, für eine Länge, deren Grössenordnung etwas grösser ist, als die der Grenzschichtdicke. Bei der Hinterkante ist das Unterschichtsproblem nicht linear, und es gibt keine analytische Lösung, aber man kann zeigen, dass die Grössenordnung der Korrektur der gesamten Wärmeübertragung etwas grösser ist als die Korrektur bei der Vorderkante. Die Strömung bei der Hinterkante ist dieselbe wie die Strömung bei der Kante einer rotierenden Scheibe in einer sonst ruhenden Flüssigkeit. Das Temperatur-Diskontinuitätsproblem ist linear, und eine Lösung ist hier gefunden worden, wodurch die von der Grenzschichttheorie gegebene Singularität (unendliche Quergeschwindigkeit) entfernt wird.

     

Toward optimal gossiping schemes with conference calls

n people have distinct bits of information which they can communicate by k-person conference calls. The object of gossip is to inform everyone of everyone else's information. Which networks admit a minimum call gossip scheme? For k = 2 a necessary and sufficient condition for such a network is that it is connected and contains a cycle of length 4. We address the same question for k>2. The values of n are partitioned into 2 classes: trivial and nontrivial. A necessary and sufficient condition is given for networks of size n for trivial n. For nontrivial n a sufficient condition is given and its necessity is conjectured.     

Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices

We demonstrate optical switching of electrically resonant terahertz planar metamaterials fabricated on ErAs/GaAs nanoisland superlattice substrates. Photoexcited charge carriers in the superlattice shunt the capacitive regions of the constituent elements, thereby modulating the resonant response of the metamaterials. A switching recovery time of 20 ps results from fast carrier recombination in the ErAs/GaAs superlattice substrates.     

The resonance energy of amides and their radical cations

Structural Chemistry - The resonance energy of an amide can be calculated through comparison with a model amine and a model ketone (or aldehyde) with subtraction of the “residual”...     

Frontispiece: From Phosphidic to Phosphonium? Umpolung of the P4-Bonding Situation in [CpFe(CO)(L)(η1-P4)]+ Cations (L=CO or PPh3)

Upon coordinating P₄ to electron poor cyclopentadienyl-iron cations, the average P−P bond distances shrink and the respective P₄ breathing mode in the Raman spectra (600 cm⁻¹, P_{4, free}) is blueshifted by >40 cm⁻¹ in [CpFe(CO)(L)(η¹-P₄)]⁺ cations (L=CO or PPh₃). Analysis suggests that this corresponds to an umpolung of the bonding from more phosphidic in the known, electron-rich systems to more phosphonium-like in the reported electron-poor versions. This may open new functionalization pathways for white phosphorus P₄.