Thermal boundary layer equation for turbulent Rayleigh-Bénard convection.

We report a new thermal boundary layer equation for turbulent Rayleigh-Bénard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr≳1 and (b) Pr≫1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol), respectively.

Heterogeneous Responses to Changes in Inhibitory Synaptic Strength in Networks of Spiking Neurons.

How does the dynamics of neurons in a network respond to changes in synaptic weights? Answer to this question would be important for a full understanding of synaptic plasticity. In this article, we report our numerical study of the effects of changes in inhibitory synaptic weights on the spontaneous activity of networks of spiking neurons with conductance-based synapses. Networks with biologically realistic features, which were reconstructed from multi-electrode array recordings taken in a cortical neuronal culture, and their modifications were used in the simulations. The magnitudes of the synaptic weights of all the inhibitory connections are decreased by a uniform amount subjecting to the condition that inhibitory connections would not be turned into excitatory ones. Our simulation results reveal that the responses of the neurons are heterogeneous: while the firing rate of some neurons increases as expected, the firing rate of other neurons decreases or remains unchanged. The same results show that heterogeneous responses also occur for an enhancement of inhibition. This heterogeneity in the responses of neurons to changes in inhibitory synaptic strength suggests that activity-induced modification of synaptic strength does not necessarily generate a positive feedback loop on the dynamics of neurons connected in a network. Our results could be used to understand the effects of bicuculline on spiking and bursting activities of neuronal cultures. Using reconstructed networks with biologically realistic features enables us to identify a long-tailed distribution of average synaptic weights for outgoing links as a crucial feature in giving rise to bursting in neuronal networks and in determining the overall response of the whole network to changes in synaptic strength. For networks whose average synaptic weights for outgoing links have a long-tailed distribution, bursting is observed and the average firing rate of the whole network increases upon inhibition suppression or decreases upon inhibition enhancement. For networks whose average synaptic weights for outgoing links are approximately normally distributed, bursting is not found and the average firing rate of the whole network remains approximately constant upon changes in inhibitory synaptic strength.

Revealing directed effective connectivity of cortical neuronal networks from measurements.

In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R) (2017)2470-004510.1103/PhysRevE.95.010301] to reveal directed effective connectivity, namely, the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of cortical regions in rats and monkeys and has similar network properties as the synaptic network of the nematode Caenorhabditis elegans, whose entire nervous system has been mapped out. The distribution of the incoming degree is bimodal and the distributions of the average incoming and outgoing synaptic strength are non-Gaussian with long tails. The effective connectivity captures different information from the commonly studied functional connectivity, estimated using statistical correlation between spiking activities. The average synaptic strengths of excitatory incoming and outgoing links are found to increase with the spiking activity in the estimated effective connectivity but not in the functional connectivity estimated using the same sets of voltage measurements. These results thus demonstrate that the reconstructed effective connectivity can capture the general properties of synaptic connections and better reveal relationships between network structure and dynamics.

Micronutrient deficiencies are frequent in adult patients with and without celiac disease on a gluten-free diet, regardless of duration and adherence to the diet.

OBJECTIVES: The only treatment for celiac disease (CD) is a strict gluten-free diet (GFD). Nutritional deficiencies are common in CD; however, how this is influenced by the presence of symptoms, duration of CD, and compliance of GFD is less clear. The objective of this study was to compare nutritional deficiencies in patients with CD to those of nonceliac populations on a GFD. The secondary outcomes were to compare deficiencies in short- (<2 y) versus long-term (≥2 y) GFD, and in those with persistent symptoms versus asymptomatic. METHODS: We included patients seen at the McMaster Celiac Clinic from June 2018 to August 2020. GFD adherence was assessed with the Celiac Dietary Adherence Test, and CD serology, vitamins, and trace minerals were measured in blood samples. We enrolled 221 patients, including 182 patients with CD and 39 controls. RESULTS: Overall, 103 of 182 patients with CD (56.6%) were following a GFD for >2 y and 119 patients (69.2%) were symptomatic. The most common micronutrient deficiencies were zinc (48.3%), ferritin (16.9%), and vitamin D (33.3%). There were no differences in micronutrient deficiencies between patients with CD and nonceliac controls, short- and long-term GFDs, or those strictly compliant with GFD and those who were fairly compliant (P > 0.05). CONCLUSIONS: These data suggest that nutrient deficiencies may be related more to GFD nutritional inadequacy rather than malabsorption.

Opioid Utilization and Management in the Setting of Stewardship During Inpatient Rehab Care.

Background: Opioid utilization and management in an inpatient rehabilitation setting have not been widely described, despite the unique opportunities that exist in this setting to support opioid stewardship across transitions in care. We aimed to characterize opioid utilization and management by interprofessional teams across a large, inpatient rehabilitation setting after incorporation of opioid stewardship principles by pharmacists as part of their daily practice. Patients and methods: This was a retrospective chart review at Toronto Rehab, University Health Network, Toronto, Canada. Patients with admission orders for any opioid from November 2017 to February 2018 were included. Complex continuing care and palliative care patients were excluded. Descriptive statistics were primarily used to describe the data as well as univariate linear regression to compare associations with milligram morphine equivalent (MME) reduction. Results: A total of 448 patients were included. A reduction in total daily MME was seen in 49% (n=219) of the patients during their inpatient stay, with 73% (n=159) of these patients having a reduction of ≥50%. Sixty-nine percent (n=311) of the patients received an opioid prescription at discharge, with most scheduled (90%, n=98) with a supply of less than 30 days. Rehabilitation length of stay was correlated with a MME decrease during rehab (p<0.01), suggesting that longer lengths of stay contributed to a greater reduction in MME. Patients with chronic opioid use prior to acute care admission (p=0.01), and those who started extended-release opioids during acute care (p=0.02) were significantly less likely to discontinue opioids during rehab stay. Conclusion: Opioid utilization and management in the setting of opioid stewardship across inpatient rehab and transitions of care were characterized. Opportunities exist for further quality improvement initiatives within inpatient rehabilitation and acute care settings to identify and support patients with complex pain management needs.

Effect of polymer additives on heat transport in turbulent thermal convection.

In this Letter, we explore the possible effects of polymer additives on heat transport in turbulent thermal convective flows. Using both direct numerical simulations and shell-model calculations, we show that polymer additives can significantly enhance the heat transport in homogeneous turbulent thermal convection, which mimics the bulk of turbulent Rayleigh-Bénard convection. We also discuss the implication of our results for turbulent Rayleigh-Bénard convection, in which there are boundary layers in addition to the central bulk.

Ultimate-state scaling in a shell model for homogeneous turbulent convection.

An interesting question in turbulent convection is how the heat transport depends on the strength of thermal forcing in the limit of very large thermal forcing. Kraichnan predicted [Phys. Fluids 5, 1374 (1962)] that for fluids with low Prandtl number (Pr), the heat transport measured by the Nusselt number (Nu) would depend on the strength of thermal forcing measured by the Rayleigh number (Ra) as Nu approximately Ra(1/2) with logarithmic corrections at very high Ra. According to Kraichnan, the shear boundary layers play a crucial role in giving rise to this so-called ultimate-state scaling. A similar scaling result is predicted by the Grossmann-Lohse theory [J. Fluid Mech. 407, 27 (2000)], but with the assumption that the ultimate state is a bulk-dominated state in which both the average kinetic and thermal dissipation rates are dominated by contributions from the bulk of the flow with the boundary layers either broken down or playing no role in the heat transport. In this paper, we study the dependence of Nu and the Reynolds number (Re) measuring the root-mean-squared velocity fluctuations on Ra and Pr, for low Pr, using a shell model for homogeneous turbulent convection where buoyancy is acting directly on most of the scales. We find that Nu approximately Ra(1/2)Pr(1/2) and Re approximately Ra(1/2)Pr(-1/2) , which resemble the ultimate-state scaling behavior for fluids with low Pr, and show that the presence of a drag acting on the large scales is crucial in giving rise to such scaling. As a large-scale drag cannot exist by itself in the bulk of turbulent thermal convection, our results indicate that if buoyancy acts on most of the scales in the bulk of turbulent convection at very high Ra, then the ultimate state cannot be bulk dominated.

Anomalous scaling and refined similarity of an active scalar in a shell model of homogeneous turbulent convection.

Anomalous scaling in the statistics of an active scalar is studied in a shell model of homogeneous turbulent convection. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent convection and attribute the origin of the anomalous scaling to variations of the entropy transfer rate. We verify the consequences and thus the validity of our hypothesis by showing that the conditional statistics of the active scalar and the velocity at fixed values of entropy transfer rate are not anomalous but have simple scaling with exponents given by dimensional considerations, and that the intermittency corrections are given by the scaling exponents of the moments of the entropy transfer rate.

Refined similarity hypotheses in shell models of homogeneous turbulence and turbulent convection.

A major challenge in turbulence research is to understand from first principles the origin of the anomalous scaling of velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. 13, 82 (1962)], which attributes the anomaly to variations of the locally averaged energy dissipation rate. Kraichnan later pointed out [J. Fluid Mech. 62, 305 (1973)] that the locally averaged energy dissipation rate is not an inertial-range quantity and a proper inertial-range quantity would be the local energy transfer rate. As a result, Kraichnan's idea attributes the anomaly to variations of the local energy transfer rate. These ideas, generally known as refined similarity hypotheses, can also be extended to study the anomalous scaling of fluctuations of an active scalar, such as the temperature in turbulent convection. We examine the validity of these refined similarity hypotheses and their extensions to an active scalar in shell models of homogeneous turbulence and turbulent convection. We find that Kraichnan's refined similarity hypothesis and its extension are valid.

Comparison of theory and direct numerical simulations of drag reduction by rodlike polymers in turbulent channel flows.

Numerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number (Re) and Deborah number (De). The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high Re and De, calls for some care. In this paper we present a study of drag reduction by rodlike polymers in a turbulent channel flow using direct numerical simulation and illustrate how these numerical results should be related to the recently developed theory.

Scaling laws in the central region of confined turbulent thermal convection.

In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focus on the plume velocity, and not the whole velocity, and the temperature when studying the scaling behavior. In this paper, a phenomenological theory for the scaling behavior in the central region of confined turbulent thermal convection is presented. The spatial (temporal) plume velocity structure functions are found to have the same scaling behavior as the spatial (temporal) temperature structure functions. For tau> or = taub, where the buoyant scale taub is determined in terms of measurable quantities, the scaling exponents of the temporal temperature structure functions and hence those of the temporal plume velocity structure functions are obtained. These results are checked against experimental measurements, and good agreement is found.

Multifractality and scale invariance in human heartbeat dynamics.

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov, Nature (London) 399, 461 (1999)]. This multifractal character could be manifested as the dependence of the probability density functions (PDFs) of the interbeat interval increments, which are the differences in two interbeat intervals that are separated by n beats, on n . On the other hand, "scale invariance in the PDFs of detrended healthy human heart rate increments" was recently reported [Kiyono, Phys. Rev. Lett. 93, 178103 (2004)]. In this paper, we clarify that the scale invariance reported is actually exhibited by the PDFs of the increments of the "detrended" integrated healthy interbeat interval and should, therefore, be more accurately referred as the scale invariance or n independence of the PDFs of the sum of n detrended interbeat intervals. Indeed, we demonstrate explicitly that the PDFs of detrended healthy interbeat interval increments are scale or n dependent in accord with its multifractal character. Our work also establishes that this n independence of the PDFs of the sum of n detrended interbeat intervals is a general feature of human heartbeat dynamics, shared by heart rate fluctuations in both healthy and pathological states.

Reconstructing links in directed networks from noisy dynamics.

We address the long-standing challenge of how to reconstruct links in directed networks from measurements, and present a general method that makes use of a noise-induced relation between network structure and both the time-lagged covariance of measurements taken at two different times and the covariance of measurements taken at the same time. When the coupling functions have certain additional properties, we can further reconstruct the weights of the links.

Turbulent drag reduction by flexible and rodlike polymers: Crossover effects at small concentrations.

Drag reduction by polymers is bounded between two universal asymptotes, the von Kármán log law of the law and the maximum drag reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The crossover behavior from the Newtonian von Kármán log law to the MDR is, however, not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this crossover phenomenology.

Turbulent Rayleigh-Bénard convection with polymers: Understanding how heat flux is modified.

We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Rayleigh numbers using direct numerical simulations with polymers of different relaxation times. We find that heat flux is enhanced by polymers and the amount of heat enhancement first increases and then decreases with the Weissenberg number, which is the ratio of the polymer relaxation time to the typical time scale of the flow. We show that this nonmonotonic behavior of the heat flux enhancement is the combined effect of the decrease in the viscous energy dissipation rate due to the viscosity of the Newtonian fluid and the increase in the energy dissipation rate due to polymers when Weissenberg number is increased. We explain why the viscous energy dissipation rate decreases with the Weissenberg number. Then by carrying out a generalized boundary layer analysis supplemented by a space-dependent effective viscosity from the numerical simulations, we provide a theoretical understanding of the change of the heat flux when the viscous energy dissipation rate is held constant. Our analysis thus provides a physical way to understand the numerical results.

Additive equivalence in turbulent drag reduction by flexible and rodlike polymers.

We address the additive equivalence discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

Reconstructing weighted networks from dynamics.

We present a method that reconstructs both the links and their relative coupling strength of bidirectional weighted networks. Our method requires only measurements of node dynamics as input. Using several examples, we demonstrate that our method can give accurate results for weighted random and weighted scale-free networks with both linear and nonlinear dynamics.