Continuum equilibria and global optimization for routing in dense static ad hoc networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton–Jacobi–Bellman equation, for the global optimization problem, (2) a method based on Green’s Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem.     

Organic magneto-resistance at small magnetic fields; compass effect

Utilizing the magneto-resistance response of organic light emitting diodes (OLEDs) at ultra-small magnetic field we show that both the value and direction of the local earth magnetic field (B_E) can be accurately obtained. We further demonstrate a ‘compass response’ in the magneto-conductance and magneto-electro-luminescence of OLEDs based on three isotopes of a π-conjugated polymer. We found that both responses are dependent on the direction of a small, fixed magnetic field B₀ (≈50 μT) with respect to B_E, and this effect is used to determine B_E direction. We conjecture that living creatures may use the same principle for magneto-reception and navigation.     

Advances in Polyimide‐Based Materials for Space Applications

The space environment raises many challenges for new materials development and ground characterization. These environmental hazards in space include solar radiation, energetic particles, vacuum, micrometeoroids and debris, and space plasma. In low Earth orbits, there is also a significant concentration of highly reactive atomic oxygen (AO). This Progress Report focuses on the development of space‐durable polyimide (PI)‐based materials and nanocomposites and their testing under simulated space environment. Commercial PIs suffer from AO‐induced erosion and surface electric charging. Modified PIs and PI‐based nanocomposites are developed and tested to resist degradation in space. The durability of PIs in AO is successfully increased by addition of polyhedral oligomeric silsesquioxane. Conductive materials are prepared based on composites of PI and either carbon nanotube (CNT) sheets or 3D‐graphene structures. 3D PI structures, which can expand PI space applications, made by either additive manufacturing (AM) or thermoforming, are presented. The selection of AM‐processable engineering polymers in general, and PIs in particular, is relatively limited. Here, innovative preliminary results of a PI‐based material processed by the PolyJet technology are presented.     

Computing discrete shape operators on general meshes

Discrete curvature and shape operators, which capture complete information about directional curvatures at a point, are essential in a variety of applications: simulation of deformable two‐dimensional objects, variational modeling and geometric data processing. In many of these applications, objects are represented by meshes. Currently, a spectrum of approaches for formulating curvature operators for meshes exists, ranging from highly accurate but computationally expensive methods used in engineering applications to efficient but less accurate techniques popular in simulation for computer graphics. We propose a simple and efficient formulation for the shape operator for variational problems on general meshes, using degrees of freedom associated with normals. On the one hand, it is similar in its simplicity to some of the discrete curvature operators commonly used in graphics; on the other hand, it passes a number of important convergence tests and produces consistent results for different types of meshes and mesh refinement.     

Reducing error in neural network time series forecasting

Neural network time series forecasting error comprises autocorrelation error, due to an imperfect model, and random noise, inherent in the data. Both problems are addressed here, the first using a two stage training, growth-network neuron: the autocorrelation error (ACE) neuron. The second is considered as a post-processing noise filtering problem. These techniques are applied in forecasting the sunspot time series, with comparison of stochastic, BFGS and conjugate gradient solvers.     

An O(n) algorithm for the linear multiple choice knapsack problem and related problems

We present an O(n) algorithm for the Linear Multiple Choice Knapsack Problem and its d-dimensional generalization which is based on Megiddo's (1982) algorithm for linear programming. We also consider a certain type of convex programming problems which are common in geometric location models. An application of the linear case is an O(n) algorithm for finding a least distance hyperplane in R^d according to the rectilinear norm. The best previously available algorithm for this problem was an O(n log²n) algorithm for the two-dimensional case. A simple application of the nonlinear case is an O(n) algorithm for finding the point at which a ‘pursuer’ minimizes its distance from the furthest among n ‘targets’, when the trajectories involved are straight lines in R^d.     

Scaling of the Shaped Charge Jet Break‐Up Time

Since the formula for the shaped charge jet break‐up time was published on 1979 many attempts were made to interpret it and to make its use more efficient. It is shown herein that the V_pl parameter depends on the ratio of the liner thickness to the charge explosive diameter by the formula: 1/V_pl=13.9−101⋅(T_L/CD), where T_L is the liner thickness, CD is the explosive charge diameter and the numbers are for a published set of measurements with an OFE copper liner driven by COMP‐B explosive. To find how the numbers used in this formula change with the liner material and its metallurgical state and with the type of explosive, measurements should be made as prescribed herein. An attempt to begin explaining this formula is made in the discussion.     

Laser-Based Printing: From Liquids to Microstructures

Assembly of materials into microstructures under laser guidance is attracting wide attention. The ability to pattern various materials and form 2D and 3D structures with micron/sub-micron resolution and less energy and material waste compared with standard top-down methods make laser-based printing promising for many applications, for example medical devices, sensors, and microelectronics. Assembly from liquids provides a smaller feature size than powders and has advantages over other states of matter in terms of relatively simple setup, easy handling, and recycling. However, the simplicity of the setup conceals a variety of underlying mechanisms, which cannot be identified simply according to the starting or resulting materials. This progress report surveys the various mechanisms according to the source of the material—preformed or locally synthesized. Within each category, methods are defined according to the driving force of material deposition. The advantages and limitations of each method are critically discussed, and the methods are compared, shedding light on future directions and developments required to advance this field.     

3D Graphene‐Infused Polyimide with Enhanced Electrothermal Performance for Long‐Term Flexible Space Applications

Polyimides (PIs) have been praised for their high thermal stability, high modulus of elasticity and tensile strength, ease of fabrication, and moldability. They are currently the standard choice for both substrates for flexible electronics and space shielding, as they render high temperature and UV stability and toughness. However, their poor thermal conductivity and completely electrically insulating characteristics have caused other limitations, such as thermal management challenges for flexible high‐power electronics and spacecraft electrostatic charging. In order to target these issues, a hybrid of PI with 3D‐graphene (3D‐C), 3D‐C/PI, is developed here. This composite renders extraordinary enhancements of thermal conductivity (one order of magnitude) and electrical conductivity (10 orders of magnitude). It withstands and keeps a stable performance throughout various bending and thermal cycles, as well as the oxidative and aggressive environment of ground‐based, simulated space environments. This makes this new hybrid film a suitable material for flexible space applications.     

Performance of ad hoc networks with two-hop relay routing and limited packet lifetime (extended version)

We consider a mobile ad hoc network consisting of three types of nodes (source, destination and relay nodes) and using the two-hop relay routing. This type of routing takes advantage of the mobility and the storage capacity of the nodes, called the relay nodes, in order to route packets between a source and a destination. Packets at relay nodes are assumed to have a limited lifetime in the network. Nodes are moving inside a bounded region according to some random mobility model. Closed-form expressions and asymptotic results when the number of nodes is large are provided for the packet delivery delay and for the energy needed to transmit a packet from the source to its destination. We also introduce and evaluate a variant of the two-hop relay protocol that limits the number of generated copies in the network. Our model is validated through simulations for two mobility models (random waypoint and random direction mobility models), and the performance of the two-hop routing and of the epidemic routing protocols are compared.