Mean Drifts Research Articles

String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor.

The kinetics of a dynamical system comprising two metastable states is formulated in terms of a finite-time propagator in phase space (position and velocity) adapted to the underdamped Langevin equation. Dimensionality reduction to a subspace of collective variables yields familiar expressions for the propagator, committor, and steady-state flux. A quadratic expression for the steady-state flux between the two metastable states can serve as a robust variational principle to determine an optimal approximate committor expressed in terms of a set of collective variables. The theoretical formulation is exploited to clarify the foundation of the string method with swarms-of-trajectories, which relies on the mean drift of short trajectories to determine the optimal transition pathway. It is argued that the conditions for Markovity within a subspace of collective variables may not be satisfied with an arbitrary short time-step and that proper kinetic behaviors appear only when considering the effective propagator for longer lag times. The effective propagator with finite lag time is amenable to an eigenvalue-eigenvector spectral analysis, as elaborated previously in the context of position-based Markov models. The time-correlation functions calculated by swarms-of-trajectories along the string pathway constitutes a natural extension of these developments. The present formulation provides a powerful theoretical framework to characterize the optimal pathway between two metastable states of a system.

A Neural Network‐Based Model for Daytime Vertical E×B Drift in the Indian Sector

AbstractObservations of ionospheric vertical E×B drift are limited in the Indian sector. In this paper, we present an artificial neural network‐based model for inferring ionospheric daytime vertical E×B drift using ground‐based magnetometer and radar observations in the Indian sector. We have used E×B drift estimated using 150‐km echoes observed by the Gadanki mesosphere‐stratosphere‐troposphere radar and the difference in ground magnetic fields (ΔH) observed from Tirunelveli (magnetic latitude 0.4°N) and Alibag (magnetic latitude 13.0°N), providing a measure of electrojet current. We have used a feed forward neural network with error back propagation to train the network and estimated E×B drifts for the period 2006–2011. The model successfully reproduces the radar‐observed vertical E×B drifts. The model E×B drifts are also found to agree exceedingly well with those measured using the CINDI onboard the C/NOFS. The model seasonal mean drifts are found to differ considerably from those of Scherliess‐Fejer model. The neural network‐based model presented here is first of its kind from the Indian sector, presenting local time, day‐to‐day, and seasonal variations of daytime equatorial F region E×B drifts during magnetically quiet conditions. Results and the potential of the model for studying equatorial electrodynamics in the Indian sector are presented.

Reverse Hardy–Littlewood–Sobolev inequalities

This paper is devoted to a new family of reverse Hardy–Littlewood–Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with free energy functionals and nonlinear diffusion equations involving mean field drifts.

Peak and residual responses of steel moment-resisting and braced frames under pulse-like near-fault earthquakes

This paper presents the behaviour of steel moment resisting and braced frames under pulse-like near-fault earthquakes. The key properties for characterizing near-fault ground motions with forward directivity and fling step effects are discussed, and the influence of varying brace properties on the key engineering demand parameters such as maximum inter-storey drift (MID), residual inter-storey drift (RID) and peak absolute floor acceleration (PA) is revealed. Among other findings, it is shown that the structural responses are related to spectral accelerations, PGV/PGA ratios, and the pulse period of near-fault ground motions. The moment resisting and self-centring braced frames (MRFs and SC-BRBFs) generally have comparable MID levels, while the buckling-restrained braced frames (BRBFs) tend to exhibit lower MIDs. Increasing the post-yield stiffness of the braces decreases the MID response. The SC-BRBFs generally have mean residual drifts less than 0.2% under all the considered ground motions. However, much larger RIDs are induced for the MRFs/BRBFs under the near-fault ground motions, suggesting that these structures may not be economically repairable after the earthquakes. From a non-structural performance point of view, the SC-BRBFs show much higher PA levels compared with the other structures. A good balance among the MID, RID, and PA responses can be achieved when “partial” SC-BRBs are used. To facilitate performance-based design, RID prediction models are finally proposed which enable an effective evaluation of the relationship between MID and RID.

Characteristics of the equatorial plasma drifts as obtained by using Canadian Doppler ionosonde over southern tip of India

AbstractWe present here characteristics of the Doppler drift measurements over Tirunelveli (8.73°N, 77.70°E; dip 0.5°N), an equatorial site over Southern India using Doppler interferometry technique of Canadian ionosonde. Three‐dimensional bulk motions of the scatterers as reflected from the ionosphere are derived by using Doppler interferometry technique at selected frequencies using spaced receivers arranged in magnetic E‐W and N‐S directions. After having compared with Lowell's digisonde drifts at Trivandrum, we studied the temporal and seasonal variabilities of quiet time drifts for the year 2012. The observations showed higher vertical drifts during post sunset in the equinox followed by winter and summer seasons. The comparison of Doppler vertical drifts with the drifts obtained from (a) virtual height and (b) Fejer drift model suggests that Doppler vertical drifts are relatively higher as compared to the drifts obtained from model and virtual height methods. Further, it is seen that vertical drifts exhibited equinoctial asymmetry in prereversal enhancement quite similar to such asymmetry observed in the spread F in the ionograms and GPS L band scintillations. The zonal drifts, on the other hand, showed westward during daytime with mean drifts of ~150–200 m/s and correlated well with equatorial electrojet strength indicating the role of E region dynamo during daytime, while they are eastward during nighttime with mean drifts of ~100 m/s resembling F region dynamo process. Also, zonal drifts showed large westward prior to the spread F onset during autumn equinox than vernal equinox, suggesting strong zonal shears which might cause equinoctial asymmetry in spread F.

Reducing the within-patient variability of breathing for radiotherapy delivery in conscious, unsedated cancer patients using a mechanical ventilator

Objective:Variability in the breathing pattern of patients with cancer during radiotherapy requires mitigation, including enlargement of the planned treatment field, treatment gating and breathing guidance interventions. Here, we provide the first demonstration of how easy it is to mechanically ventilate patients with breast cancer while fully conscious and without sedation, and we quantify the resulting reduction in the variability of breathing.Methods:15 patients were trained for mechanical ventilation. Breathing was measured and the left breast anteroposterior displacement was measured using an Osiris surface-image mapping system (Qados Ltd, Sandhurst, UK).Results:Mechanical ventilation significantly reduced the within-breath variability of breathing frequency by 85% (p < 0.0001) and that of inflation volume by 29% (p < 0.006) when compared with their spontaneous breathing pattern. During mechanical ventilation, the mean amplitude of the left breast marker displacement was 5 ± 1 mm, the mean variability in its peak inflation position was 0.5 ± 0.1 mm and that in its trough inflation position was 0.4 ± 0.0 mm. Their mean drifts were not significantly different from 0 mm min−1 (peak drift was −0.1 ± 0.2 mm min−1 and trough drift was −0.3 ± 0.2 mm min−1). Patients had a normal resting mean systolic blood pressure (131 ± 5 mmHg) and mean heart rate [75 ± 2 beats per minute (bpm)] before mechanical ventilation. During mechanical ventilation, the mean blood pressure did not change significantly, mean heart rate fell by 2 bpm (p < 0.05) with pre-oxygenation and rose by only 4 bpm (p < 0.05) during pre-oxygenation with hypocapnia. No patients reported discomfort and all 15 patients were always willing to return to the laboratory on multiple occasions to continue the study.Conclusion:This simple technique for regularizing breathing may have important applications in radiotherapy.Advances in knowledge:Variations in the breathing pattern introduce major problems in imaging and radiotherapy planning and delivery and are currently addressed to only a limited extent by asking patients to breathe to auditory or visual guidelines. We provide the first demonstration that a completely different technique, of using a mechanical ventilator to take over the patients' breathing for them, is easy for patients who are conscious and unsedated and reduces the within-patient variability of breathing. This technique has potential advantages in radiotherapy over currently used breathing guidance interventions because it does not require any active participation from or feedback to the patient and is therefore worthy of further clinical evaluation.

Seismic behavior of viscously damped yielding frames under structural and damping uncertainties

This paper examines the sensitivity of the response of optimally damped frames to uncertainty in structural and damping properties. Viscous dampers are first optimally designed for given nominal properties of the retrofitted structures and a given ensemble of records for each structure. The behavior of the retrofitted structures (in terms of the maximum envelope peak inter-story drift) considering uncertainty in their properties as well as in the dampers’ properties is then tested using Monte Carlo simulation. It is shown that the uncertainties lead to larger mean drifts than expected, and that some designs are more sensitive than others. The physical reasons for this behavior are discussed and some rules as to what designs are expected to be more sensitive are given.

Excursions and path functionals for stochastic processes with asymptotically zero drifts

We study discrete-time stochastic processes (Xt) on [0,∞) with asymptotically zero mean drifts. Specifically, we consider the critical (Lamperti-type) situation in which the mean drift at x is about c/x. Our focus is the recurrent case (when c is not too large). We give sharp asymptotics for various functionals associated with the process and its excursions, including results on maxima and return times. These results include improvements on existing results in the literature in several respects, and also include new results on excursion sums and additive functionals of the form ∑s≤tXsα, α>0. We make minimal moments assumptions on the increments of the process. Recently there has been renewed interest in Lamperti-type process in the context of random polymers and interfaces, particularly nearest-neighbour random walks on the integers; some of our results are new even in that setting. We give applications of our results to processes on the whole of R and to a class of multidimensional ‘centrally biased’ random walks on Rd; we also apply our results to the simple harmonic urn, allowing us to sharpen existing results and to verify a conjecture of Crane et al.

Moments of Exit Times from Wedges for Non-homogeneous Random Walks with Asymptotically Zero Drifts

We study quantitative asymptotics of planar random walks that are spatially non-homogeneous but whose mean drifts have some regularity. Specifically, we study the first exit time τ α from a wedge with apex at the origin and interior half-angle α by a non-homogeneous random walk on ℤ2 with mean drift at x of magnitude O(∥x∥−1) as ∥x∥→∞. This is the critical regime for the asymptotic behaviour: under mild conditions, a previous result of the authors stated that τ α <∞ a.s. for any α. Here we study the more difficult problem of the existence and non-existence of moments \({\mathbb{E}}[ \tau_{\alpha}^{s}]\), s>0. Assuming a uniform bound on the walk’s increments, we show that for α<π/2 there exists s 0∈(0,∞) such that \({\mathbb{E}}[ \tau_{\alpha}^{s}]\) is finite for s<s 0 but infinite for s>s 0; under specific assumptions on the drift field, we show that we can attain \({\mathbb{E}}[ \tau_{\alpha}^{s}] = \infty\) for any s>1/2. We show that there is a phase transition between drifts of magnitude O(∥x∥−1) (the critical regime) and o(∥x∥−1) (the subcritical regime). In the subcritical regime, we obtain a non-homogeneous random walk analogue of a theorem for Brownian motion due to Spitzer, under considerably weaker conditions than those previously given (including work by Varopoulos) that assumed zero drift.

Random Walk with Barycentric Self-interaction

We study the asymptotic behaviour of a d-dimensional self-interacting random walk (X n ) n∈ℕ (ℕ:={1,2,3,…}) which is repelled or attracted by the centre of mass $G_{n} = n^{-1} \sum_{i=1}^{n} X_{i}$ of its previous trajectory. The walk’s trajectory (X 1,…,X n ) models a random polymer chain in either poor or good solvent. In addition to some natural regularity conditions, we assume that the walk has one-step mean drift $$\mathbb{E}[X_{n+1} - X_n \mid X_n - G_n = \mathbf{x}] \approx\rho\|\mathbf{x}\|^{-\beta}\hat{ \mathbf{x}}$$ for ρ∈ℝ and β≥0. When β<1 and ρ>0, we show that X n is transient with a limiting (random) direction and satisfies a super-diffusive law of large numbers: n −1/(1+β) X n converges almost surely to some random vector. When β∈(0,1) there is sub-ballistic rate of escape. When β≥0 and ρ∈ℝ we give almost-sure bounds on the norms ‖X n ‖, which in the context of the polymer model reveal extended and collapsed phases. Analysis of the random walk, and in particular of X n −G n , leads to the study of real-valued time-inhomogeneous non-Markov processes (Z n ) n∈ℕ on [0,∞) with mean drifts of the form 0.1 $$ \mathbb{E}[ Z_{n+1} - Z_n \mid Z_n = x ] \approx\rho x^{-\beta} - \frac {x}{n},$$ where β≥0 and ρ∈ℝ. The study of such processes is a time-dependent variation on a classical problem of Lamperti; moreover, they arise naturally in the context of the distance of simple random walk on ℤ d from its centre of mass, for which we also give an apparently new result. We give a recurrence classification and asymptotic theory for processes Z n satisfying (0.1), which enables us to deduce the complete recurrence classification (for any β≥0) of X n −G n for our self-interacting walk.

Identifying the time of polynomial drift in the mean of autocorrelated processes

AbstractControl charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special ause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. This paper addresses change point estimation for covariance‐stationary autocorrelated processes where the mean drifts deterministically with time. For example, the mean of a chemical process might drift linearly over time as a result of a constant pressure leak. The goal of this paper is to derive and evaluate an MLE for the time of polynomial drift in the mean of autocorrelated processes. It is assumed that the behavior in the process mean over time is adequately modeled by the kth‐order polynomial trend model. Further, it is assumed that the autocorrelation structure is adequately modeled by the general (stationary and invertible) mixed autoregressive‐moving‐average model. The estimator is intended to be applied to data obtained following a genuine control chart signal in efforts to help pinpoint the root cause of process change. Application of the estimator is demonstrated using a simulated data set. The performance of the estimator is evaluated through Monte Carlo simulation studies for the k=1 case and across several processes yielding various levels of positive autocorrelation. Results suggest that the proposed estimator provides process engineers with an accurate and useful estimate for the last sample obtained from the unchanged process. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Stability Criteria for Multi-class Queueing Networks with Re-entrant Lines

In this paper we show how the stability criteria for the model proposed in MacPhee and Muller (Queueing Syst 52(3):215–229, 2006) can be applied to queueing networks with re-entrant lines. The model considered has Poisson arrival streams, servers that can be configured in various ways, exponential service times and Markov feedback of completed jobs. The stability criteria are expressed in terms of the mean drifts of the process under the various server configurations. For models with re-entrant lines we impose here a boundary sojourn condition to ensure adequate control of the process when one or more queues are empty. We show with some examples, including the generalised Lu–Kumar network discussed in Nino-Mora and Glazebrook (J Appl Probab 37(3):890–899, 2000), how our results can be applied.

The Cape Cauldron: a regime of turbulent inter-ocean exchange

Combining in-situ Lagrangian intermediate depth velocity measurements from the KAPEX (Cape of Good Hope Experiments) float program with sea-surface height data, this study reviews the inter-ocean exchange mechanisms around southern Africa. In the southeastern Cape Basin, a highly energetic field of coexisting anticyclonic and cyclonic eddies is documented. Agulhas Rings of typically 200 km diameter are observed to merge, split, deform, and to reconnect to the Agulhas Retroflection. Concomitant, slightly smaller cyclones are observed to drift across the northwestward migration path of the Agulhas Rings. These cyclones, with typical diameters of 120 km, are formed within the Cape Basin along the African shelf, inshore of the Agulhas Current, and in the subantarctic region south of Africa. The data suggest the annual formation of 3–6 long-lived Agulhas Rings that eventually cross 5°E longitude, while approximately twice the number of rings occur in the southeastern Cape Basin. Within this region, cyclones outnumber anticyclones by a factor of 3:2. Both cyclones and anticyclones extend through the upper thermocline into the intermediate depth layer. Mean drifts of anticyclones are 3.8±1.2 cm s−1 to the northwest, while cyclones follow a west–southwestward route at 3.6±0.8 cm s−1. Transport estimates suggest that the intermediate depth layer in the southeastern Cape Basin is primarily supplied from the east (approximately 9 Sv), with minor direct inflow from the Atlantic to the west and south. Cyclone/anticyclone interaction is surmised to result in vigorous stirring and mixing processes in the southeastern Cape Basin, which necessitates a review of the traditional concept of Indo-Atlantic inter-ocean exchange. We propose to limit the concept of “isolated Agulhas Rings embedded in a sluggish Benguela Drift” to the northwestern Cape Basin and beyond, while linking this regime to the Agulhas Retroflection proper through a zone of turbulent stirring and mixing in the southeastern Cape Basin, named for the first time the “Cape Cauldron” hereinafter.

Inverse reliability-based design of shear buildings supported by springs with stochastic stiffnesses

A straightforward and efficient stiffness design method is developed for a shear building supported by a pair of swaying and rocking springs with stiffnesses given as statistically independent normal variates. The story stiffnesses are determined with the use of the closed form stiffness solution for specified fundamental frequency and translational eigenmode so that the probability of the seismic mean maximum interstory drifts not exceeding prescribed values would coincide with the specified value. The proposed method consists of two steps: (1) find the stiffnesses of swaying and rocking springs that can achieve the constrained nonexceedance probability by derived approximate formulas; (2) determine the story stiffnesses of the shear building so that the mean maximum interstory drifts would coincide with the prescribed values. The validity and good accuracy of the proposed method are demonstrated by use of Monte Carlo simulation.

The western boundary current of the seasonal subtropical gyre in the Bay of Bengal

Hydrographic data collected during March–April 1991 show the presence of a poleward current along the western boundary of the Bay of Bengal north of about 10° N carrying warmer waters of southern origin. The inshore side of the current was marked by cooler, more saline waters brought to the surface due to the presence of the current which transported approximately 10 × 106 m3/s. The hydrography is suggestive of many of the features that have been associated with the western boundary currents of the subtropical gyres of the world oceans: a recirculation zone, waves, eddies, etc. These features, however, were not satisfactorily resolved in the data. Using available climatologies of monthly mean ship drifts, seasonal hydrography, and monthly mean wind stress, we propose that the poleward current is the western boundary current of a seasonal anticyclonic subtropical gyre which forms in the Bay during January, is best developed during March‐April, and decays by June. The gyre and the western boundary current are unique because of their seasonal character. The pattern of circulation leading to formation and decay of the gyre is reproduced reasonably well in the computation of the monthly mean barotropic transport induced by the curl of wind stress, which has a well‐defined annual cycle due to the monsoons and which is conducive to the formation of an anticyclonic gyre only during the months of January‐May. The pattern of circulation due to baroclinic transport induced by the wind stress curl, however, is not known at present, and this makes it difficult to conclude unequivocally that the wind stress curl over the bay is the sole mechanism to force the gyre.

Stiffness Design of 3‐D Shear Buildings for Specified Seismic Drifts

The closed‐form solution is derived to the problem of stiffness design of coaxially coeccentric asymmetric shear buildings (CCS buildings) for specified fundamental natural frequency and eigenvector. The complete quadratic combination (CQC) estimates of the mean maximum interstory drifts in a so‐designed CCS building subjected to an ensemble of design‐spectrum‐compatible moderate earthquakes are regarded as functions of the lowest eigenvalue and translational eigenvector, parameters for adjustment of those CQC estimates. An almost direct and efficient method of stiffness design is developed for a CCS building such that all the CQC estimates of the mean maximum drifts of the corner columns based upon a prescribed design spectrum will be equal to the prescribed distribution of design drifts. The validity of the design procedure is demonstrated with the results of time history analysis on so‐designed CCS buildings. A design amplifier factor for specified distribution of lateral torsional drifts is defined and is shown to be useful for describing directly the effect of eccentricity on the seismic response‐drift constrained designs of CCS buildings.

Technical Note—Mean Drifts and the Non-Ergodicity of Markov Chains

An important question in stochastic modeling is whether or not a denumerable state Markov chain is ergodic. We extend a result of Kaplan giving a condition for the non-ergodicity of a chain based on its drifts. We also clarify the condition under which the mean drift in the stationary chain is zero.

Asymmetry of the Internal Seiche in Loch Ness

LOCH NESS seems to be particularly suitable for internal wave research. Because it is freshwater the effects of salinity, which are so difficult to monitor in the ocean, are absent. The wind has a strongly preferred direction up and down the length of the steep-sided Loch, which is of a fairly regular shape (Fig. 1) and great depth, and which supports a well developed thermocline and rich microstructure1 in the late summer. Long range effects and mean drifts (other than those associated with the rivers and streams which enter or leave the Loch) which occur in the ocean are absent, and so the Loch provides an excellent open air laboratory for testing theories of internal wave generation, propagation and decay.

The equilibrium drift of Ice Station Alpha

The problem of the equilibrium (unaccelerated) drift of an ice floe (no internal resistance) is solved by a treatment similar to Shuleikin's. Curves of drift angle, drift speed, and wind factor as functions of wind speed are computed for two different sets of parameters and compared with Shuleikin's curves for one of the sets. As a test of the theory, drift angles, drift speeds, and wind factors were plotted against wind speed for 107 periods between July 1, 1957, and August 31, 1958, in which the drift of station Alpha was essentially unaccelerated. The data exhibited considerable scatter, and it was necessary to compute mean drifts in various wind categories in order to bring out the empirical relationships. The observed drift angles were smaller than the theoretical in all wind categories, though the departures were not as great for our curves as for Shuleikin's curve. The graphs of drift speed and wind factors also exhibited systematic deviations from the theoretical curves, the ice drifting faster than the theoretical speed in light winds and slower in strong winds. In explaining the deviations between observation and theory six sources of error are considered: navigation errors, errors due to residual accelerations, errors due to use of averaged data, errors due to variations in parameters, errors caused by gradient currents, and errors attributable to internal stresses. Although part of the scatter is found to be the result of the navigation errors, it is concluded that gradient currents and internal stresses are probably the main causes of drift anomalies. Evidence from the present study and from other sources suggests that a permanent current of about 3 cm sec−1 exists in the region of the drift of Alpha. This would account for the above-normal drift in light winds. The below-normal drift in strong winds is believed to be the result of internal resistance, though tests failed to show this conclusively.