scholarly journals Equilibrium fluctuations in maximally noisy extended quantum systems

2019 ◽  
Vol 6 (4) ◽  
Author(s):  
Michel Bauer ◽  
Denis Bernard ◽  
Tony Jin
Keyword(s):  
Steady State ◽  
Matrix Theory ◽  
Large Deviation ◽  
System Size ◽  
Deviation Function ◽  
Magnitude Scaling ◽  
The Mean ◽  
Large System Size ◽  
Occupancy Profile ◽  
System Approaches

We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by an integral with respect to the unitary Haar measure, known as the Harish-Chandra-Itzykson-Zuber integral in random matrix theory, which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. Diagrammatic tools appropriate for the study of these correlations are presented. In the thermodynamic large system size limit, the system approaches a non random, self averaging, equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that sub-leading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

Evaluation of Single-Hole Hydraulic Tests in Fractured Crystalline Rock by Steady-State and Transient Methods: A Comparison

1985 ◽  
Vol 50 ◽  
Author(s):  
J-E. Andersson ◽  
O. Persson
Keyword(s):  
Steady State ◽  
Hydraulic Conductivity ◽  
Flow Pattern ◽  
Transient Analysis ◽  
Crystalline Rock ◽  
Steady State Analysis ◽  
Single Hole ◽  
The Mean ◽  
Transient Methods ◽  
State Analysis

AbstractThe results from a large number of single-hole packer tests in crystalline rock from three test sites in Sweden have been analysed statistically. Average hydraulic conductivity values for 25 m long test intervals along boreholes with a maximal length of about 700 m are used in this study. A comparison between steady state and transient analysis of the same test data has been performed.The mean vaule of the hydraulic conductivity determined from steady state analysis was found to be about two to three times higher compared to transient analysis. However, in some cases the steady state analysis resulted in 10 to 20 times higher values compared to the transient analysis. Such divergence between the two analysis methods may be caused by deviations from the assumed flow pattern, borehole skin effects and influence of hydraulic boundaries.

A numerical study of the sedimentation of fibre suspensions

1998 ◽  
Vol 376 ◽  
pp. 149-182 ◽  
Author(s):  
MICHAEL B. MACKAPLOW ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Numerical Study ◽  
Point Particle ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Fibre Suspensions ◽  
The Mean

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

scholarly journals Vertical Round Buoyant Jets and Fountains in a Linearly, Density-Stratified Fluid

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 232
Author(s):  
Panos N. Papanicolaou ◽  
George C. Stamoulis
Keyword(s):  
Steady State ◽  
Laboratory Experiments ◽  
Coefficient Function ◽  
Buoyant Jets ◽  
Asymptotic Values ◽  
Entrainment Coefficient ◽  
Source Level ◽  
The Mean ◽  
Negatively Buoyant ◽  
Negatively Buoyant Jets

Turbulent round buoyant jets and fountains issuing vertically into a linearly density-stratified calm ambient have been investigated in a series of laboratory experiments. The terminal (steady-state) height of rise and the mean elevation of subsequent horizontal spreading have been measured in positively buoyant jets (at source level), including pure momentum jets and plumes, as well in momentum-driven negatively buoyant jets (fountains). The results from experiments confirmed the asymptotic analysis that was based on dimensional arguments. The normalized terminal height and spreading elevation with respect to the elevation of injection of momentum-driven (positively) buoyant jets and fountains attained the same asymptotic values. The numerical results from the solution of entrainment equations, using an improved entrainment coefficient function, confirmed the results related to buoyancy dominant flows (plumes), while their predictions in momentum-driven flows were quite low if compared to measurements.

Steady-state twitch Ca2+ fluxes and cytosolic Ca2+ buffering in rabbit ventricular myocytes

1996 ◽  
Vol 270 (1) ◽  
pp. C192-C199 ◽  
Author(s):  
L. M. Delbridge ◽  
J. W. Bassani ◽  
D. M. Bers
Keyword(s):  
Steady State ◽  
Sarcoplasmic Reticulum ◽  
Voltage Clamp ◽  
Ventricular Myocytes ◽  
Cell Voltage ◽  
Whole Cell ◽  
Rabbit Ventricular Myocytes ◽  
The Mean ◽  
State Contraction ◽  
Caffeine Contractures

Intracellular Ca2+ ([Ca2+]i) transients and transsarcolemmal Ca2+ currents were measured in indo 1-loaded isolated rabbit ventricular myocytes during whole cell voltage clamp to quantitate the components of cytosolic Ca2+ influx and to describe the dynamic aspects of cytosolic Ca2+ buffering during steady-state contraction (0.5 Hz, 22 degrees C). Sarcolemmal Ca2+ influx was directly measured from the integrated Ca2+ current (Ica) recorded during the clamp (158 +/- 10 attomoles; amol). Sarcoplasmic reticulum (SR) Ca2+ content was determined from the integrated electrogenic Na+/Ca2+ exchange current (Ix) induced during rapid application and sustained exposure of cells to caffeine to elicit the release of the SR Ca2+ load (1,208 +/- 170 amol). The mean steady-state SR Ca2+ load was calculated to be 87 +/- 13 microM (mumol/l nonmitochondrial cytosolic volume). Ca2+ influx via Ica represented approximately 14% of the stored SR Ca2+ and 23% of the total cytosolic Ca2+ flux during a twitch (47 +/- 6 microM). Comparison of electrophysiologically measured Ca2+ fluxes with Ca2+ transients yields apparent buffering values of 60 for caffeine contractures and 110 for twitches (delta Ca2+ total/delta Ca2+ free). This is consistent with the occurrence of "active" buffering of cytosolic Ca2+ by SR Ca2+ uptake during the twitch.

Topographic Analysis of Steady-State Visual Evoked Potentials (SVEPs) in The Medium Frequency Range in Migraine With and Without Aura

Cephalalgia ◽  
1992 ◽  
Vol 12 (4) ◽  
pp. 244-249 ◽  
Author(s):  
Franco M Puca ◽  
Marina de Tommaso ◽  
Maria A Savarese ◽  
Sergio Genco ◽  
Addolorata Prudenzano
Keyword(s):  
Steady State ◽  
Frequency Range ◽  
Medium Frequency ◽  
Topographic Analysis ◽  
Absolute Power ◽  
Interhemispheric Coherence ◽  
The Mean ◽  
Student’S T ◽  
Medium Frequency Range ◽  
Student’S T Test

Topographic analysis of SVEPs in the medium frequencies range was performed in 30 migraineurs without aura, 20 migraineurs with aura and in 20 control subjects. The mean absolute power values of the fundamental component F1, the subharmonic F1/2 and the first harmonic F2, corrected by logarithmic transformation, were computed in each group and then compared using Student's t-test. The interhemispheric coherence of the F1 component was also evaluated. The 18, 21 and 27 Hz F1 components were increased in both migraineurs with and without aura, particularly in the temporo-parietal regions. The 24 Hz F1 component was augmented only in migraineurs without aura in the parieto-occipital regions in comparison with migraineurs with aura and controls. Migraine with aura patients had a reduced interhemispheric coherence mostly of 12 Hz and 15 Hz F1 components in frontal and temporo-parietal regions. Results of the study confirm abnormalities of SVEPs in migraineurs with and without aura. These consist of widespread increases of F1 components in the medium frequency range over the temporo-parietal regions.

scholarly journals Comparison of Plasma, Epithelial Lining Fluid, and Alveolar Macrophage Concentrations of Solithromycin (CEM-101) in Healthy Adult Subjects

2012 ◽  
Vol 56 (10) ◽  
pp. 5076-5081 ◽  
Author(s):  
Keith A. Rodvold ◽  
Mark H. Gotfried ◽  
J. Gordon Still ◽  
Kay Clark ◽  
Prabhavathi Fernandes
Keyword(s):  
Steady State ◽  
High Performance ◽  
Healthy Adult ◽  
Plasma Concentrations ◽  
Epithelial Lining ◽  
Time Curve ◽  
Epithelial Lining Fluid ◽  
Once Daily ◽  
Drug Concentrations ◽  
The Mean

ABSTRACTThe steady-state concentrations of solithromycin in plasma were compared with concomitant concentrations in epithelial lining fluid (ELF) and alveolar macrophages (AM) obtained from intrapulmonary samples during bronchoscopy and bronchoalveolar lavage (BAL) in 30 healthy adult subjects. Subjects received oral solithromycin at 400 mg once daily for five consecutive days. Bronchoscopy and BAL were carried out once in each subject at either 3, 6, 9, 12, or 24 h after the last administered dose of solithromycin. Drug concentrations in plasma, ELF, and AM were assayed by a high-performance liquid chromatography-tandem mass spectrometry method. Solithromycin was concentrated extensively in ELF (range of mean [± standard deviation] concentrations, 1.02 ± 0.83 to 7.58 ± 6.69 mg/liter) and AM (25.9 ± 20.3 to 101.7 ± 52.6 mg/liter) in comparison with simultaneous plasma concentrations (0.086 ± 0.070 to 0.730 ± 0.692 mg/liter). The values for the area under the concentration-time curve from 0 to 24 h (AUC0–24values) based on mean and median ELF concentrations were 80.3 and 63.2 mg · h/liter, respectively. The ratio of ELF to plasma concentrations based on the mean and median AUC0–24values were 10.3 and 10.0, respectively. The AUC0–24values based on mean and median concentrations in AM were 1,498 and 1,282 mg · h/L, respectively. The ratio of AM to plasma concentrations based on the mean and median AUC0–24values were 193 and 202, respectively. Once-daily oral dosing of solithromycin at 400 mg produced steady-state concentrations that were significantly (P< 0.05) higher in ELF (2.4 to 28.6 times) and AM (44 to 515 times) than simultaneous plasma concentrations throughout the 24-h period after 5 days of solithromycin administration.

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