On the Impact of Geometry on Ad Hoc Communication in Wireless Networks

In this work we address the question how important is the knowledge of geometric location and network density to the efficiency of (distributed) wireless communication in ad hoc networks. We study fundamental communication task of broadcast and develop well-scalable, randomized algorithms that do not rely on GPS information, and which efficiency formulas do not depend on how dense the geometric network is. We consider two settings: with and without spontaneous wake-up of nodes. In the former setting, in which all nodes start the protocol at the same time, our algorithm accomplishes broadcast in $O(D\log n + \log^2 n)$ rounds under the SINR model, with high probability (whp), where $D$ is the diameter of the communication graph and $n$ is the number of stations. In the latter setting, in which only the source node containing the original message is active in the beginning, we develop a slightly slower algorithm working in $O(D\log^2 n)$ rounds whp. Both algorithms are based on a novel distributed coloring method, which is of independent interest and potential applicability to other communication tasks under the SINR wireless model

The role of traction in membrane curvature generation.

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape

Mechanisms of Actomyosin Contractility in Cells

Many fundamental cellular processes hinge on the ability of cells to exert contractile force. Contractility is used by cells to divide, to migrate, to heal wounds, and to pump the heart and move limbs. Contractility is mediated by the actin and myosin cytoskeleton, a dynamic and responsive meshwork that assembles into various well-defined structures used by the cell to accomplish specific tasks. While muscle contraction is well-characterized, the contraction mechanisms of actomyosin structures in nonmuscle cells are relatively obscure. Here we elucidate the contraction mechanisms of two prominent and related actomyosin structures: the contractile ring, which constricts to divide the cell during cytokinesis, and the stress fiber, which is anchored to the extracellular matrix and allows the cell to exert contractile forces on its surroundings. In the first part of the thesis, we develop a mathematical model to characterize the constriction mechanism of contractile rings in the Schizosaccharomyces pombe model organism. Our collaborators observed that after digesting the cell wall to create protoplasts, contractile rings constricted by sliding along the plasma membrane without cleaving the cell. This novel approach allowed direct comparison of our model predictions for the ring constriction rate and ring shape to the experimental data, and demonstrated that the contractile ring's rate of constriction is determined by a balance between ring tension and external resistance forces. Our results describe a casual relationship between ring organization, actin turnover kinetics, tension, and constriction. Ring tension depends on ring organization through the actin and myosin concentrations and their statistical correlations. These correlations are established and renewed by actin turnover on a timescale much less than the constriction time so that rapid actin turnover sets the tension and provides the mechanism for continuous remodeling during constriction. Thus, we show that the contractile ring is a tension-producing machine regulated by actin turnover whose constriction rate depends on the response of a coupled system to the ring tension. In the second part of the thesis we examine the contraction mechanisms of stress fibers, which have a sarcomeric structure reminiscent of muscle. We developed mathematical models of stress fibers to describe their rapid shortening after severing and to describe how the kinetics of sarcomere contraction and expansion depend on actin turnover. To test these models, we performed quantitative image analysis of stress fibers that spontaneously severed and recoiled. We observed that after spontaneous severing, stress fibers shorten by ~80% over ~15-30 s, during which ~50% of the actin initially present was disassembled. Actin disassembly was delayed by ~50 s relative to fiber recoil, causing a characteristic increase, peak, and decay in the actin density after severing. Model predictions were in excellent agreement with the observations. The model predicts that following breakage, fiber shortening due to myosin contractile force increases actin filament overlap in the center of the sarcomeres, which in turn causes compressive actin-actin elastic stresses. These stresses promote actin disassembly, thereby shortening the actin filaments and allowing further contraction. Thus, the model identifies a mechanism whereby coupling between actin turnover and mechanical stresses allows stress fibers to dynamically adjust actin filament lengths to accommodate contraction

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

In-situ measurement of journal bearing lubricant viscosity by means of a novel ultrasonic measurement technique using matching layer

An ultrasonic viscometer was used to measure the circumferential viscosity variation in a journal bearing non-invasively. This sensing technique is based on the reflection of a shear wave at a solid-liquid boundary that depends on the viscosity of the liquid and the acoustic properties of the solid. Very little ultrasonic energy can propagate into the oil at a metal-oil interface because the acoustic mismatch is significant. Interleaving a matching layer between the metal and the lubricant enables accurate ultrasonic viscosity measurements [1] Schirru, M., Mills, R., Dwyer-Joyce, R., Smith, O., and Sutton, M. (2015). Viscosity Measurement in a Lubricant Film Using an Ultrasonically Resonating Matching Layer. Tribology Letters, 60(3) pp. 1–11. [CrossRef], [Web of Science ®] . This technique has been used to build a miniaturized ultrasonic viscometer that is accommodated inside a journal to obtain the circumferential viscosity profile. Four viscosity regions are identified due to the variations in the localized temperatures and loads. The results are compared with the isothermal solution of the Reynolds equations for hydrodynamic lubricated bearings. The ultrasonic viscometer locates the angle at which the maximum load occurs and the length of the loaded contact with good accuracy. Finally, the viscosity results are used to estimate the frictional power losses. It is shown that over 70% of the total losses in the journal bearing occur in the region where the load is maximum

Mid-Lift-to-Drag Ratio Rigid Vehicle Control System Design and Simulation for Human Mars Entry

The Mid-Lift-to-Drag Ratio Rigid Vehicle (MRV) is a proposed candidate in the NASA Evolvable Mars Campaign's (EMC) Pathfinder Entry, Descent, and Landing (EDL) architecture study. The purpose of the study is to design a mission and vehicle capable of transporting a 20mt payload to the surface of Mars. The MRV is unique in its rigid, asymmetrical lifting-body shape which enables a higher lift-to-drag ratio (L/D) than the typical robotic Mars entry capsule vehicles that carry much less mass. This paper presents the formulation and six-degree-of-freedom (6DOF) performance of the MRV's control system, which uses both aerosurfaces and a propulsive reaction control system (RCS) to affect longitudinal and lateral directional behavior

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio