Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow. This is the case for mammals respiration for which air has to reach the gas exchange units before the start of expiration. We report here that introducing a systematic branching asymmetry allows to reduce the average delivery time of the products. It simultaneously increases its robustness against the unevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to fit with the asymmetry measured in the human lung. This could indicate that the structure is adjusted at the maximum asymmetry level that allows to feed all terminal units with fresh air.Comment: 4 pages, 4 figure

A note on compactly generated co-t-structures

The idea of a co-t-structure is almost "dual" to that of a t-structure, but with some important differences. This note establishes co-t-structure analogues of Beligiannis and Reiten's corresponding results on compactly generated t-structures.Comment: 10 pages; details added to proofs, small correction in the main resul

Neurophysiology

Contains reports on one research project.Bell Telephone Laboratories (Grant

Role of Nanoscale Roughness in the Heat Transfer Characteristics of Thin Film Evaporation

Thin film evaporation yields high local heat fluxes that contributes significantly to the total heat transfer rate during various two-phase transport processes including pool boiling, flow boiling, and droplet evapo- ration, among others. Recent studies have shown a strong correlation between the roughness of a surface and its two-phase heat transfer characteristics, but the underlying role of nanoscale surface roughness in thin film evaporation is not fully understood. In the present work, a thin film evaporation model is developed that accounts for the role of the roughness-affected disjoining pressure and flow permeability in determining the film thickness profile and heat transfer rate. Nanoscale surface roughness leads to a flatter evaporating meniscus profile when the effect of disjoining pressure is more pronounced of the two and promotes evaporation, consistent with previous experimental observations. However, our results reveal that surface roughness may also inhibit evaporation and lead to a steeper evaporating meniscus profile when flow permeability has the more pronounced influence on thin film evaporation. It is impor- tant to identify the specific surface roughness characteristics that determine whether disjoining pressure or flow permeaiblity has the stronger influence. To this end, a parametric study is performed that ana- lyzes thin film evaporation on V-grooved surfaces of different depths and pitches. While the heat transfer rate increases monotonically with groove depth, there exists an optimal groove pitch that leads to a max- imized evaporation rate. Also, when the groove pitch is smaller than a critical value, surface roughness inhibits thin film evaporation

Analytical prediction of stress and strain in adhesive tube-to-tube joints under thermal expansion/contraction

Adhesive joints are widely applied and studied for various industrial applications. The interest in adhesive joints has expanded to include heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems having a significant number of joints employed for manufacturing. This study investigates an analytical modeling approach for predicting joint stress and strain distribution under static loading with thermal strain. A review of modeling techniques identified the need to develop a joint analytical model under loading conditions representative of HVAC&R applications. The details of the model, governing equations, assumptions, boundary conditions, and solution techniques are first reported. The model is validated via comparison to existing results before performing parametric studies to provide insights on the influences of thermal expansion and inner tube pressure on possible failure. It is found that the joint overlap length plays an important role in stress distribution, while the adhesive thickness has less impact. Overall, the results indicate that static loading failure is not likely a concern for joints in HVAC&R systems, but the thermal strain and stress induced by temperature fluctuations must be carefully considered. This modeling effort establishes a framework that can be used to generate criteria and instructions on designing adhesive joints across different HVAC&R</p

A figure of merit to characterize the efficacy of evaporation from porous microstructured surfaces

Evaporation from porous structured surfaces is encountered in a variety of applications including electronics cooling, desalination, and solar energy generation. Of major interest in the design of thermal systems for such applications is a prediction of the heat and mass transfer rates during evaporation from these surfaces. The present study develops a figure of merit (FOM) that characterizes the efficacy of evaporative heat transfer from microstructured surfaces. Geometric quantities such as the contact line length per unit area, porosity, and contact angle that are independent of details of the surface structure are utilized to develop the FOM, allowing for flexibility in its application to a variety of structured surfaces. This metric is calibrated against an evaporative heat transfer model and further benchmarked with evaporation heat transfer data from the literature. The FOM successfully captures the variation in evaporation heat transfer coefficient across different structures as well as the optimum dimensions for a given structure, and therefore can serve as a tool to survey available structures and also optimize their dimensions for heat and mass transfer enhancement

Particle Acceleration, Magnetic Field Generation, and Emission in Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of ``jitter'' radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.Comment: 6 pages, 1 figure, revised and accepted for Advances in Space Research (35th COSPAR Scientific Assembly, Paris, 18-25 July 2004

Prediction of Air-Side Particulate Fouling of HVAC&R Heat Exchangers

Air-to-refrigerant heat exchangers used in heating, ventilation, air-conditioning, and refrigeration systems routinely experience air-side fouling due to the presence of particulates in outdoor and indoor environments. The influence on the performance of the heat exchanger, in terms of heat transfer efficiency and pressure drop imposed, depends on the extent of air-side fouling. Fouling of a heat exchanger is determined by a variety of parameters such as the dimensions of the heat exchanger, physical properties of the airborne particulates, and airflow conditions over the heat exchange surfaces. A comprehensive model is developed to deterministically calculate the extent of fouling of a heat exchanger as a function of these parameters by accounting for each of the possible deposition mechanisms. The study enhances modeling approaches previously employed in the literature by accounting for time-dependent accumulation of particles as well as the effects of the streamwise distribution of accumulated dust on subsequent fouling; the calculations for the deposition due to several of the mechanisms are also refined to improve prediction accuracy. Particulate matter deposits already present on the surface are found to accelerate the process of fouling by decreasing available area for airflow; an existing deposit layer effectively decreases the distance that a particle must travel to collide with a surface and increases the surface area available for deposition. The modified model predictions are compared against extant experimental deposition fraction data; an improved agreement is observed compared to previous models in the literature

A Coboundary Morphism For The Grothendieck Spectral Sequence

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Comment: 18 page