Wireless scheduling with partial channel state information: large deviations and optimality

We consider a server serving a time-slotted queued system of multiple packet-based flows, where not more than one flow can be serviced in a single time slot. The flows have exogenous packet arrivals and time-varying service rates. At each time, the server can observe instantaneous service rates for only a subset of flows ( selected from a fixed collection of observable subsets) before scheduling a flow in the subset for service. We are interested in queue length aware scheduling to keep the queues short. The limited availability of instantaneous service rate information requires the scheduler to make a careful choice of which subset of service rates to sample. We develop scheduling algorithms that use only partial service rate information from subsets of channels, and that minimize the likelihood of queue overflow in the system. Specifically, we present a new joint subset-sampling and scheduling algorithm called Max-Exp that uses only the current queue lengths to pick a subset of flows, and subsequently schedules a flow using the Exponential rule. When the collection of observable subsets is disjoint, we show that Max-Exp achieves the best exponential decay rate, among all scheduling algorithms that base their decision on the current ( or any finite past history of) system state, of the tail of the longest queue. To accomplish this, we employ novel analytical techniques for studying the performance of scheduling algorithms using partial state, which may be of independent interest. These include new sample-path large deviations results for processes obtained by non-random, predictable sampling of sequences of independent and identically distributed random variables. A consequence of these results is that scheduling with partial state information yields a rate function significantly different from scheduling with full channel information. In the special case when the observable subsets are singleton flows, i.e., when there is effectively no a priori channel state information, Max-Exp reduces to simply serving the flow with the longest queue; thus, our results show that to always serve the longest queue in the absence of any channel state information is large deviations optimal.

Experimental studies on the flow through soft tubes and channels

Experiments conducted in channels/tubes with height/diameter less than 1 mm with soft walls made of polymer gels show that the transition Reynolds number could be significantly lower than the corresponding value of 1200 for a rigid channel or 2100 for a rigid tube. Experiments conducted with very viscous fluids show that there could be an instability even at zero Reynolds number provided the surface is sufficiently soft. Linear stability studies show that the transition Reynolds number is linearly proportional to the wall shear modulus in the low Reynolds number limit, and it increases as the 1/2 and 3/4 power of the shear modulus for the `inviscid' and `wall mode' instabilities at high Reynolds number. While the inviscid instability is similar to that in the flow in a rigid channel, the mechanisms of the viscous and wall mode instabilities are qualitatively different. These involve the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The experimental results for the viscous instability mechanism are in quantitative agreement with theoretical predictions. At high Reynolds number, the instability mechanism has characteristics similar to the wall mode instability. The experimental transition Reynolds number is smaller, by a factor of about 10, than the theoretical prediction for the parabolic flow through rigid tubes and channels. However, if the modification in the tube shape due to the pressure gradient, and the consequent modification in the velocity profile and pressure gradient, are incorporated, there is quantitative agreement between theoretical predictions and experimental results. The transition has important practical consequences, since there is a significant enhancement of mixing after transition.

Two-Phase Flow With Phase Change in Porous Channels

Phase change heat transfer in porous media finds applications in various geological flows and modern heat pipes. We present a study to show the effect of phase change on heat transfer in a porous channel. We show that the ratio of Jakob numbers based on wall superheat and inlet fluid subcooling governs the liquid-vapor interface location in the porous channel and below a critical value of the ratio, the liquid penetrates all the way to the extent of the channel in the flow direction. In such cases, the Nusselt number is higher due to the proximity of the liquid-vapor interface to the heat loads. For higher heat loads or lower subcooling of the liquid, the liquid-vapor interface is pushed toward the inlet, and heat transfer occurs through a wider vapor region thus resulting in a lower Nusselt number. This study is relevant in the designing of efficient two-phase heat exchangers such as capillary suction based heat pipes where a prior estimation of the interface location for the maximum heat load is required to ensure that the liquid-vapor interface is always inside the porous block for its operation.

Effect of absolute pressure on flow through a textured hydrophobic microchannel

The potential of textured hydrophobic surfaces to provide substantial drag reduction has been attributed to the presence of air bubbles trapped on the surface cavities. In this paper, we present results on water flow past a textured hydrophobic surface, while systematically varying the absolute pressure close to the surface. Trapped air bubbles on the surface are directly visualized, along with simultaneous pressure drop measurements across the surface in a microchannel configuration. We find that varying the absolute pressure within the channel greatly influences the trapped air bubble behavior, causing a consequent effect on the pressure drop (drag). When the absolute pressure within the channel is maintained below atmospheric pressure, we find that the air bubbles grow in size, merge and eventually detach from the surface. This growth and subsequent merging of the air bubbles leads to a substantial increase in the pressure drop. On the other hand, a pressure above the atmospheric pressure within the channel leads to gradual shrinkage and eventual disappearance of trapped air bubbles. We find that in this case, air bubbles do cause reduction in the pressure drop with the minimum pressure drop (or maximum drag reduction) occurring when the bubbles are flush with the surface. These results show that the trapped air bubble dynamics and the pressure drop across a textured hydrophobic microchannel are very significantly dependent on the absolute pressure within the channel. The results obtained hold important implications toward achieving sustained drag reduction in microfluidic applications.

Ischaemic concentrations of lactate increase TREK1 channel activity by interacting with a single histidine residue in the carboxy terminal domain

Key points The physiological metabolite, lactate and the two-pore domain leak potassium channel, TREK1 are known neuroprotectants against cerebral ischaemia. However, it is not known whether lactate interacts with TREK1 channel to provide neuroprotection. In this study we show that lactate increases TREK1 channel activity and hyperpolarizes CA1 stratum radiatum astrocytes in hippocampal slices. Lactate increases open probability and decreases longer close time of the human (h)TREK1 channel in a concentration dependent manner. Lactate interacts with histidine 328 (H328) in the carboxy terminal domain of hTREK1 channel to decrease its dwell time in the longer closed state. This interaction was dependent on the charge on H328. Lactate-insensitive mutant H328A hTREK1 showed pH sensitivity similar to wild-type hTREK1, indicating that the effect of lactate on hTREK1 is independent of pH change. AbstractA rise in lactate concentration and the leak potassium channel TREK1 have been independently associated with cerebral ischaemia. Recent literature suggests lactate to be neuroprotective and TREK1 knockout mice show an increased sensitivity to brain and spinal cord ischaemia; however, the connecting link between the two is missing. Therefore we hypothesized that lactate might interact with TREK1 channels. In the present study, we show that lactate at ischaemic concentrations (15-30mm) at pH7.4 increases TREK1 current in CA1 stratum radiatum astrocytes and causes membrane hyperpolarization. We confirm the intracellular action of lactate on TREK1 in hippocampal slices using monocarboxylate transporter blockers and at single channel level in cell-free inside-out membrane patches. The intracellular effect of lactate on TREK1 is specific since other monocarboxylates such as pyruvate and acetate at pH7.4 failed to increase TREK1 current. Deletion and point mutation experiments suggest that lactate decreases the longer close dwell time incrementally with increase in lactate concentration by interacting with the histidine residue at position 328 (H328) in the carboxy terminal domain of the TREK1 channel. The interaction of lactate with H328 is dependent on the charge on the histidine residue since isosteric mutation of H328 to glutamine did not show an increase in TREK1 channel activity with lactate. This is the first demonstration of a direct effect of lactate on ion channel activity. The action of lactate on the TREK1 channel signifies a separate neuroprotective mechanism in ischaemia since it was found to be independent of the effect of acidic pH on channel activity. Key points The physiological metabolite, lactate and the two-pore domain leak potassium channel, TREK1 are known neuroprotectants against cerebral ischaemia. However, it is not known whether lactate interacts with TREK1 channel to provide neuroprotection. In this study we show that lactate increases TREK1 channel activity and hyperpolarizes CA1 stratum radiatum astrocytes in hippocampal slices. Lactate increases open probability and decreases longer close time of the human (h)TREK1 channel in a concentration dependent manner. Lactate interacts with histidine 328 (H328) in the carboxy terminal domain of hTREK1 channel to decrease its dwell time in the longer closed state. This interaction was dependent on the charge on H328. Lactate-insensitive mutant H328A hTREK1 showed pH sensitivity similar to wild-type hTREK1, indicating that the effect of lactate on hTREK1 is independent of pH change.

The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1, infinity)-RLL constraint. We derive the capacity for this setting, which can be expressed as C-is an element of = max(0 <= p <= 0.5) (1-is an element of) H-b (p)/1+(1-is an element of) p, where is an element of is the erasure probability and Hb(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.