Critical Time Scale Research Articles

A time-scale decomposition approach to measurement-based admission control

We propose a time-scale decomposition approach to measurement-based admission control (MBAC). We identify a critical time scale, T/spl tilde//sub h/, such that: 1) aggregate traffic fluctuations slower than T/spl tilde//sub h/ can be tracked by the admission controller and compensated for by flow admissions and departures; 2) fluctuations faster than T/spl tilde//sub h/ have to be absorbed by reserving spare bandwidth on the link. The critical time scale is shown to scale as T/sub h///spl radic/n, where T/sub h/ is the average flow duration and n is the size of the link in terms of the number of flows it can carry. An MBAC design is presented which filters aggregate measurements into low- and high-frequency components separated at the cutoff frequency, 1/T/spl tilde//sub h/, using the low-frequency component to track slow time-scale traffic fluctuations and the high-frequency component to estimate the spare bandwidth needed. Our analysis shows that the scheme achieves high utilization and is robust to traffic heterogeneity, multiple time-scale fluctuations and measurement errors. The scheme uses only measurements of aggregate bandwidth and does not need to keep track of per-flow information.

ChandraObservations of the Disruption of the Cool Core in A133

We present the analysis of a Chandra observation of the galaxy cluster A133, which has a cooling flow core, a central radio source, and a diffuse, filamentary radio source that has been classified as a radio relic. The X-ray image shows that the core has a complex structure. The most prominent feature is a of emission that extends from the central cD galaxy to the northwest and partly overlaps the radio relic. Spectral analysis shows that the emission from the tongue is thermal emission from relatively cool gas at a temperature of ~1.3 keV. One possibility is that this tongue is produced by Kelvin-Helmholtz (KH) instabilities through the interaction between the cold gas around the cD galaxy and hot intracluster medium. We estimate the critical velocity and timescale for the KH instability to be effective for the cold core around the cD galaxy. We find that the KH instability can disrupt the cold core if the relative velocity is 400 km s-1. We compare the results with those of clusters in which sharp, undisrupted cold fronts have been observed; in these clusters, the low-temperature gas in their central regions has a more regular distribution. In contrast to A133, these cluster cores have longer timescales for the disruption of the core by the KH instability when they are normalized to the timescale of the cD galaxy motion. Thus, the other cores are less vulnerable to KH instability. Another possible origin of the tongue is that it is gas that has been uplifted by a buoyant bubble of nonthermal plasma that we identify with the observed radio relic. From the position of the bubble and the radio estimate of the age of the relic source, we estimate a velocity of ~700 km s-1 for the bubble. The structure of the bubble and this velocity are consistent with numerical models for such buoyant bubbles. The energy dissipated by the moving bubble may affect the cooling flow in A133. The combination of the radio and X-ray observations of the radio relic suggest that it is a relic radio lobe formerly energized by the central cD rather than a merger shock-generated cluster radio relic. The lobe may have been displaced from the central cD galaxy by the motion of the cD galaxy or by the buoyancy of the lobe.

An Emerging Concept of Biomolecular Dynamics and Function: Applications of NMR & MRI

A new concept of protein dynamics has emerged quite recently, and a crucial link between protein dynamics and function has been largely established using recent NMR techniques in the solution state. Protein structure is governed by the thermodynamic principle and may not necessarily be unique in the solution state. Enzyme catalysis, protein folding or allosteric transition occurs on the microsecond to millisecond time scale, implying that in order to prepare the specific nuclear coordinate for the electronic state transition, a protein must rearrange its nuclear coordinates substantially, and this process may generally take a long period of time almost comparable to that of protein folding. Protein coordinates optimized for the electronic reaction may form an energy state--which may be called an "excited state"--that is thermodynamically distinct from the native state. In contrast, the native state is called a "ground state." Relevant NMR techniques developed recently may also have useful application to MRI, since the critical time scale of various reactions in a living system is also around micro- to milliseconds.

Adhesion Frequency in Interfacial Dynamics of Copolymers

This paper introduces the concept of adhesion frequency that characterizes the dynamic interaction between a polymer matrix and a solid surface. It is argued that the pressure sensitive bonding of a polymer interface occurs within a critical time scale below which no wetting is established upon contact. The adhesion frequency can be viewed as the inverse of this critical time scale. The bonding kinetics is used to model transient adhesion and take into account the growth of bonding energy with time. The mechanics of the interfacial dynamics is used to derive expressions for the adhesion frequency when inertial, viscous or elastic effects dominate the surface deformation. Transient adhesion effects are also investigated experimentally using non-axisymmetric rotating bits and commercially-available copolymer adhesives. The rotating bits induce an oscillatory motion on the polymer surface. Experiments are conducted with the rotating bits spinning at a wide range of speeds making it possible to obtain the dynamic response of the polymer interface as well as to measure the adhesion frequency for the tested polymers.

The role of time in toxicology or Haber’s c× t product

It happened exactly 100 years ago that Warren established for the first time a quantitative link between dose and time while studying the toxicity of sodium chloride in Daphnia magna (Straus). During this century many toxicologists in different contexts returned to this idea, which has become known as Haber’s rule of inhalation toxicology. Most attempts to explore this relationship ended in frustration because of the supposed occurrence of exceptions. Thus, toxicologists concentrated on the quantitative relationship between dose and effect under mostly isotemporal conditions while time took a back seat and was assigned such arbitrary, semiquantitative designations as acute, subacute, subchronic and chronic. Time itself as a quantifiable variable of toxicity was seldom studied and when it was studied, it was often not under isodosic (steady state) conditions as required by theory. A recent analysis of toxicological time indicated the impact of three independent time scales (toxicokinetic, toxicodynamic, exposure frequency/duration) in toxicological studies, which interact with dose and effect to yield the enormous complexity known to every toxicologist. Based on prototypical examples when toxicokinetic (dioxins), toxicodynamic (nitrosamines, benzene) or exposure frequency (methylene chloride, chloroacetic acid, HgCl 2, CdCl 2, etc.) represent the critical time scale, the general validity of the c× t= k concept will be discussed as a starting point for a theory of toxicology. As endpoints of toxicity, (delayed) acute toxicity, blood dyscrasias and cancer will be used to illustrate the critical conditions needed to demonstrate the validity of this theory.

Extinction of turbulent counterflow flames under periodic strain

The effects of imposed oscillations on the extinction of turbulent nonpremixed and premixed counterflow flames have been quantified as a function of amplitude and frequency of the oscillation. Forced flame extinction was shown to depend on the total duration of pulsation and ranged from a few milliseconds to almost a second, depending on the amplitude and the frequency of the oscillation. Thus extinction times increased quasi-exponentially with decreasing amplitude and increasing frequency of oscillation for nonpremixed flames but were a nonmonotonic function of frequency in premixed flames, with the longest extinction time corresponding to higher frequencies as the flame tended to stoichiometric. Premixing of the fuel or the air stream increased the stability of forced flames, with extinction times reaching their maximum values for twin stoichiometric flames and decreasing towards leaner or richer mixtures. Velocity measurements revealed that the rms of the velocity fluctuations due to the imposed forcing was comparable to, or larger than, the bulk velocity so that oscillated flames were subjected to and survived instantaneous strain rates which were higher than those which caused extinction of the corresponding unforced flames. Visualization showed that the instantaneous strain rate was up four times that of the bulk flow for about half the oscillation period and promoted flame extinction during this part of the oscillation cycle. However, if the duration of the oscillation was smaller than a critical time scale, extinction did not occur, revealing that there was weakening of the flame over several cycles during which the temperature was reduced.

A framework for robust measurement-based admission control

Measurement-based admission control (MBAC) is an attractive mechanism to concurrently offer quality of service (QoS) to users, without requiring a priori traffic specification and on-line policing. However, several aspects of such a system need to be dearly understood in order to devise robust MBAC schemes, i.e., schemes that can match a given QoS target despite the inherent measurement uncertainty, and without the tuning of external system parameters. We study the impact of measurement uncertainty, flow arrival, departure dynamics, and of estimation memory on the performance of a generic MBAC system in a common analytical framework. We show that a certainty equivalence assumption, i.e., assuming that the measured parameters are the real ones, can grossly compromise the target performance of the system. We quantify the improvement in performance as a function of the length of the estimation window and an adjustment of the target QoS. We demonstrate the existence of a critical time scale over which the impact of admission decisions persists. Our results yield new insights into the performance of MBAC schemes, and represent quantitative and qualitative guidelines for the design of robust schemes.

Femtosecond dynamics of diradicals: transition states, entropic configurations and stereochemistry

With femtosecond-resolved mass spectrometry, we report real-time studies of the dynamics of reactive diradicals: trimethylene, tetramethylene and structurally-constrained (by a bridge) tetramethylene. These comparative studies elucidate the role of transition states, entropic configurations and IVR on the global potential energy surface. The critical time scale for rotational clocks in stereochemistry is illustrated in the reaction mechanism for cyclization and fragmentation products.

Reorientational Dynamics of Cyclohexadienyl Radicals in High-Silica ZSM-5

The avoided-level-crossing relaxation of a polarized muon spin-label was used to investigate the reorientational dynamics of muonated cyclohexadienyl radicals in NaZSM-5 with SiO2/Al2O3 ratios of 670 and 900 and loadings of one and two benzene molecules per unit cell. It was found that on a critical time scale of about 50 ns the radical performs fast uniaxial rotation about the axis perpendicular to the molecular plane. Superimposed on this there is a two-site jump motion between two orientations that differ by an angle of 110° and 1.0 kJ mol-1 in energy. This causes increasing averaging of the orientations above 50 K. It is particularly extensive but still not isotropic in a temperature range between 200 and 450 K. Below 50 K, the uniaxial rotation slows down below the critical time scale of the experiment, and below 20 K any motion is frozen. It is suggested that such a high reorientational mobility is possible only for the radicals occupying sites at the channel intersections. Above ca. 450 K, the reve...

Dynamical systems of Langevin type

Dynamical systems of Langevin type are deterministic mappings that arise if the Gaussian white noise of a Langevin equation is replaced by a deterministic chaotic dynamics. We describe the various types of mappings that can be obtained in this way, and investigate typical transition scenarios from complicated non-Gaussian to Langevin-like behavior that occur if a time scale parameter is changed. We define a new characteristic quantify fir ergodic mappings called ‘effective Langevin radius’, which is related to the critical time scale where the marginal invariant density of the dynamical system of Langevin type loses its differentiability. The invariant density is shown to contain useful information on the entire characteristic functional of the chaotic driving force. Some general symmetry properties of the invariant densities are discussed.

Law and the Regulatory Environment of Waste Management

The management of waste, along with a variety of other issues impacting on the environment, has now arrived centre stage in a fast-developing agenda for the environment. In contemporary terms, the critical time-scale for any meaningful examination of the law's policy and technique stretches from the Control of Pollution Act 1974, enacted just after British accession to the European Economic Community, to the present when, at the time of writing, the Environmental Protection Bill is about to be enacted and the Government's promised White Paper on the environment has been published. From this cross-roads there is a very interesting view of progress in the task of managing waste through the law's facilities. It is the task of this case study to map the unfolding of what, hitherto, has been a very traditional 'axis' for the law's approach to waste management. In crude terms that axis has emphasised the (statutory) regulatory environment under Part I of the Control of Pollution Act 1974 and the available common law techniques for the distribution of liabilities. The central question to be asked here is whether this axis can be developed adequately for the purpose of coping with increasing anxieties about the treatment and management of waste. This central question begs a variety of other questions, all of which have to be addressed in this attempt to evaluate the law as an instrument (and perhaps the most important instrument) for the imposition and proper enforcement of responsibilities in the present context. To what extent should economic instruments seek to replace or complement traditional legal regulation here? To what extent should a private law contractual approach seek to supplement traditional public law-based regulatory techniques, where the powers of the regulator are often closely confined by the relevant statutory authority? Is there an effective collaboration between these public law-based regulatory techniques and the private (common) law rules of tort, ensuring a rather more automatic distribution of 'real' liability in the wake of failures to follow the regulatory code? Underlying many of these questions are further questions about the limits of law enforcement in the field of waste management as well as the status and influence of EEC law.