Robust method of manufacturing rubber waste‐based water repellent surfaces

A novel method of rubber waste recycling is presented. Shredded rubber is processed into a biomimetic superhydrophobic material demonstrating high apparent contact angles (APCAs). Wetting properties of the obtained surfaces are reported. The presented method of rubber waste processing is robust, inexpensive and promises a good potential for building industry. Copyright © 2008 John Wiley & Sons, Ltd.     

The Gibbs Cloner for Combinatorial Optimization, Counting and Sampling

We present a randomized algorithm, called the cloning algorithm, for approximating the solutions of quite general NP-hard combinatorial optimization problems, counting, rare-event estimation and uniform sampling on complex regions. Similar to the algorithms of Diaconis–Holmes–Ross and Botev–Kroese the cloning algorithm is based on the MCMC (Gibbs) sampler equipped with an importance sampling pdf and, as usual for randomized algorithms, it uses a sequential sampling plan to decompose a “difficult” problem into a sequence of “easy” ones. The cloning algorithm combines the best features of the Diaconis–Holmes–Ross and the Botev–Kroese. In addition to some other enhancements, it has a special mechanism, called the “cloning” device, which makes the cloning algorithm, also called the Gibbs cloner fast and accurate. We believe that it is the fastest and the most accurate randomized algorithm for counting known so far. In addition it is well suited for solving problems associated with the Boltzmann distribution, like estimating the partition functions in an Ising model. We also present a combined version of the cloning and cross-entropy (CE) algorithms. We prove the polynomial complexity of a particular version of the Gibbs cloner for counting. We finally present efficient numerical results with the Gibbs cloner and the combined version, while solving quite general integer and combinatorial optimization problems as well as counting ones, like SAT.     

Self-force of a charge in a real current

The analysis of the EM radiation from a single charge shows that the radiated power depends on the retarded acceleration of the charge. Therefore for consistency, an accelerated charge, free from the influence of external forces, should gradually lose its acceleration, until its total energy is radiated. Calculations show that the self force of a charge, which compensates for its radiation, is proportional to the derivative of the acceleration. However, when using this self force in the equation of motion of the charge, one gets a diverging solution, for which the acceleration runs away to infinity. This means that there is an inconsistency in the solution of the single charge problem. However, in the construction of the conserved Maxwell charge density, there is implicitly an integral over the corresponding world line which corresponds to a collection of charged spacetime events. One may therefore consistently think of the “self force” as the force on a charge due to another charge at the retarded position. From this point of view, the energy is evidently conserved and the radiation process appears as an absorbing resistance to the feeding source. The purpose of this work is to learn about the behavior of single charges from the behavior of a real current, corresponding to the set of charges moving on a world line, and to study the analog of the self force of a charge associated with the radiation resistance of a continuum of charges.     

Exploiting locality: approximating sorting buffers

The sorting buffers problem is motivated by many applications in manufacturing processes and computer science, among them car-painting and file servers architecture. The input is a sequence of items of various types. All the items must be processed, one by one, by a service station. We are given a random-access sorting buffer with a limited capacity. Whenever a new item arrives it may be moved directly to the service station or stored in the buffer. Also, at any time items can be removed from the buffer and assigned to the service station. Our goal is to give the service station a sequence of items with minimum type transitions. We generalize the problem to allow items with different sizes and type transitions with different costs. We give a polynomial-time 9-approximation algorithm for the maximization variant of this problem, which improves the best previously known 20-approximation algorithm.     

Nondifferentiable optimization via smooth approximation: General analytical approach

In this paper we present a method for nondifferentiable optimization, based on smoothed functionals which preserve such useful properties of the original function as convexity and continuous differentiability. We show that smoothed functionals are convenient for implementation on computers. We also show how some earlier results in nondifferentiable optimization based on smoothing-out of kink points can be fitted into the framework of smoothed functionals. We obtain polynomial approximations of any order from smoothed functionals with kernels given by Beta distributions. Applications of smoothed functionals to optimization of min-max and other problems are also discussed.     

Energy Mechanism of Charges Analyzed in Real Current Environment

We analyze in this work the energy transfer process of accelerated charges, the mass fluctuations accompanying this process, and their inertial properties. Based on a previous work, we use here the dipole antenna, which is a very convenient framework for such analysis, for analyzing those characteristics. We show that the radiation process can be viewed by two energy transfer processes: one from the energy source to the charges and the second from the charges into the surrounding space. Those processes, not being in phase, result in mass fluctuations. The same principle is true during absorption. We show that in a transient period between absorption and radiation the dipole antenna gains mass according to the amount of absorbed energy and loses this mass as radiated energy. We rigorously prove that the gain of mass, resulting from electrical interaction has inertial properties in the sense of Newton's third low. We arrive to this result by modeling the reacting spacetime region by an electric dipole.     

Scale-free networks are ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-free networks with 23, d approximately ln(N. We also show that, for any lambda>2, one can construct a deterministic scale-free network with d approximately ln(ln(N, which is the lowest possible diameter.     

Computer simulation of an energy transfer dye laser (ETDL)

Computer calculations of an energy transfer dye laser (ETDL) performance are presented. It is shown that the ETDL output can be manipulated by varying the donor or acceptor concentrations. Experiments done on the anthracene-perylene ETDL are in agreement with the predictions of the present calculation.     

Velocities, Stresses and Vector Bundle Valued Chains

A mathematical framework for the fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, velocity fields over bodies, modeled as sections of a vector bundle W, are generalized using notions of homological integration theory such as flat chains and cochains. The class of bodies includes fractal sets whose irregular boundaries may have infinite measures. Stresses, initially modeled as smooth differential forms valued in the dual of the jet bundle of W, are generalized to cochains represented by L ^??-sections whose weak divergences are also L ^??. The divergence of a stress field, defined in an earlier work, is generalized to apply to stress cochains. The co-divergence of a velocity field is a weak form of the jet extension mapping and it is the counterpart of the boundary operator for real valued flat chains.