Online Bin Stretching with Three Bins

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of $11/8 = 1.375$ for three bins. Additionally, we present a lower bound of $45/33 = 1.\overline{36}$ for Online Bin Stretching on three bins and a lower bound of $19/14$ for four and five bins that were discovered using a computer search.Comment: Preprint of a journal version. See version 2 for the conference paper. Conference paper split into two journal submissions; see arXiv:1601.0811

Online Bin Stretching: Algoritmy a strojové dolní odhady

Online Bin Stretching: algoritmy a strojové dolní odhady Autor: Martin Böhm Abstrakt: Zabýváme se problémem v oblasti semi-online algoritmů, který se nazývá Online Bin Stretching. Můžeme tento problém chápat jako pro- blém opětovného pakování předmětů: cílem algoritmu je zapakovat před- měty různých velikostí do m kontejnerů identické kapacity R > 1. Objekty na vstupu přicházejí jeden po druhém a algoritmus musí přiřadit předmět do kontejneru dříve, než se objeví předmět další. Zvláštnost tohoto konkrétního problému je existence zaručené vlastnosti vstupu, kterou algoritmus zná. Algoritmus totiž už od začátku vstupu má zaručeno, že existuje pakování celého vstupu do m kontejnerů kapacity 1. Naším cílem je navrhnout algoritmy, které pakují jeden objekt po dru- hém a kterým se podaří vstup zapakovat do co nejmenší možné kapacity R. V této dizertační práci představíme několik nových výsledků kolem On- line Bin Stretchingu. Zaprvé, navrhneme algoritmus, který napakuje všechny objekty do m kontejnerů s kapacitou 1,5, a to pro libovolnou počáteční hodnotu m. Zadruhé se soustředíme na podproblém, ve kterém je počet kontejnerů nízký a pevný, například 3. Pro tento model představíme algo- ritmus, který zapakuje vstup do 3 binů s kapacitou 1,375. Nakonec navrhneme a naimplementujeme počítačový program, který bude...Online Bin Stretching: Algorithms and Computer Lower Bounds Author: Martin Böhm Abstract: We investigate a problem in semi-online algorithm design, called Online Bin Stretching. The problem can be understood as an online repacking problem: the goal of the algorithm is to repack items of various sizes into m containers of identical size R > 1. The input items arrive one by one and the algorithm must assign an item to a container before the next item arrives. A specialty of this problem is that there is a specific guarantee made to the algorithm: the algorithm learns at the start of the input that there exists a packing of all input items into m containers of capacity 1. Our goal is to design algorithms for this problem which successfully pack the entire incoming sequence one by one while requiring the lowest container capacity R possible. In this thesis, we show several new results about Online Bin Stretching: First, we design an algorithm that is able to pack the entire input into m containers of capacity 1.5 regardless of what the vale of m will be. Second, we show a specialized algorithm for the setting of just 3 containers; this algorithm is able to pack into 3 bins of capacity 1.375. Finally, we design and implement an involved search algorithm which is able to find lower bounds for Online Bin...Informatický ústav Univerzity KarlovyComputer Science Institute of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Length-scale cascade and spread rate of atomizing planar liquid jets

The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier-Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number ($Re$), Weber number ($We$), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface structures, e.g. lobes, ligaments and droplets, are compared for different flow conditions and are explained in terms of the vortex dynamics in each atomization domain that we identified recently. With increasing $We$, the average radius of curvature of the surface decreases, the number of small droplets increases, and the cascade and the surface area growth occur at faster rates. The spray angle is mainly affected by $Re$ and density ratio, and is larger at higher $We$, at higher density ratios, and also at lower $Re$. The change in the spray spread rate versus $Re$ is attributed to the angle of ligaments stretching from the jet core, which increases as $Re$ decreases. Gas viscosity has negligible effect on both the droplet-size distribution and the spray angle. Increasing the wavelength-to-sheet-thickness ratio, however, increases the spray angle and the structure cascade rate, while decreasing the droplet size. The smallest length scale is determined more by surface tension and liquid inertia than by the liquid viscosity, while gas inertia and liquid surface tension are the key parameters in determining the spray angle.Comment: Submitted for publication to International Journal of Multiphase Flow. 37 pages; 33 figure

Precision cosmography with stacked voids

We present a purely geometrical method for probing the expansion history of the Universe from the observation of the shape of stacked voids in spectroscopic redshift surveys. Our method is an Alcock-Paczynski (AP) test based on the average sphericity of voids posited on the local isotropy of the Universe. It works by comparing the temporal extent of cosmic voids along the line of sight with their angular, spatial extent. We describe the algorithm that we use to detect and stack voids in redshift shells on the light cone and test it on mock light cones produced from N-body simulations. We establish a robust statistical model for estimating the average stretching of voids in redshift space and quantify the contamination by peculiar velocities. Finally, assuming that the void statistics that we derive from N-body simulations is preserved when considering galaxy surveys, we assess the capability of this approach to constrain dark energy parameters. We report this assessment in terms of the figure of merit (FoM) of the dark energy task force and in particular of the proposed EUCLID mission which is particularly suited for this technique since it is a spectroscopic survey. The FoM due to stacked voids from the EUCLID wide survey may double that of all other dark energy probes derived from EUCLID data alone (combined with Planck priors). In particular, voids seem to outperform Baryon Acoustic Oscillations by an order of magnitude. This result is consistent with simple estimates based on mode-counting. The AP test based on stacked voids may be a significant addition to the portfolio of major dark energy probes and its potentialities must be studied in detail.Comment: 16 pages, 12 figures, 2 tables; accepted by ApJ; this version reflects the accepted version, conclusions unchange

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform within a finite support in an incompressible flow, advection in the flow will give rise to inhomogeneities in the observed density. In this paper we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting towards a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet.Comment: 56 pages, 17 figure

Mechanical Stretching of Proteins: Calmodulin and Titin

Mechanical unfolding of several domains of calmodulin and titin is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. It is shown that this simple model captures the experimentally observed difference between the two proteins: titin is a spring that is tough and strong whereas calmodulin acts like a weak spring with featureless force-displacement curves. The difference is related to the dominance of the alpha secondary structures in the native structure of calmodulin. The tandem arrangements of calmodulin unwind simultaneously in each domain whereas the domains in titin unravel in a serial fashion. The sequences of contact events during unraveling are correlated with the contact order, i.e. with the separation between contact making amino acids along the backbone in the native state. Temperature is found to affect stretching in a profound way.Comment: To be published in a special bio-issue of Physica A; 14 figure

Development of a twin-head infusion pump for micromixing

Mixing is a crucial process in most of the industrial technology such as the operation of chemicals and fermentation reactors, combustion engines, polymer blends, and pharmaceutical formulations [1]. For handling a smaller volume of liquid, micromixing is a suitable method that can be applied. Micromixing (micromixer) is one of the microfluidic functions for mixing and blending liquids as precursors for biological process such as cell activation, enzyme reaction, and drug delivery system [2, 3]. There are several advantages of applying microfluidic device (micromixer) in the chemical technological processes such as processing accuracy, efficiency, minimum usage of reagents and ease of disposing of devices and fluids [3]. Basically, micromixers are categorised into passive and active micromixers. Passive micromixer consists of no moving parts and free from additional friction. It does not use external forces, fully dependent on molecular diffusion and chaotic advection for mixing process [4]. In contrast to active micromixers, external forces are applicable to active micromixers by implementing moving elements either within the microchannels, a time-variant, or a pressure field [5]. To create the pressure field differences for moving the liquid within the micromixer, an infusion pump is usually applied