scholarly journals Weighted Voronoi Diagrams in the Maximum Norm

2019 ◽  
Vol 29 (03) ◽  
pp. 239-250
Author(s):  
Günther Eder ◽  
Martin Held
Keyword(s):  
Simple Formula ◽  
Voronoi Diagrams ◽  
Incremental Algorithm ◽  
Maximum Norm ◽  
Worst Case ◽  
Line Segments ◽  
One Dimensional ◽  
Straight Line ◽  
Dimensional Version ◽  
The One

We consider multiplicatively weighted points, axis-aligned rectangular boxes and axis-aligned straight-line segments in the plane as input sites and study Voronoi diagrams of these sites in the maximum norm. For [Formula: see text] weighted input sites we establish a tight [Formula: see text] worst-case bound on the combinatorial complexity of their Voronoi diagram and introduce an incremental algorithm that allows its computation in [Formula: see text] time. Our approach also yields a truly simple [Formula: see text] algorithm for solving the one-dimensional version of this problem, where all weighted sites lie on a line.

Continuation of potential fields between arbitrary surfaces

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 787-795 ◽  
Author(s):  
R. O. Hansen ◽  
Y. Miyazaki
Keyword(s):  
Volcanic Rocks ◽  
Potential Fields ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Aeromagnetic Data ◽  
Line Segments ◽  
One Dimensional ◽  
Straight Line ◽  
The One ◽  
Topographic Relief

An equivalent source algorithm is described for continuing either one‐ or two‐dimensional potential fields between arbitrary surfaces. In the two‐dimensional case, the dipole surface is approximated as a set of plane faces with constant moments over each face. In the one‐dimensional case, the plane faces of the dipole surface reduce to straight line segments. Application of the algorithm to model and field examples of aeromagnetic data shows the method to be effective and accurate even when the terrain has strong topographic relief and is composed of highly magnetic volcanic rocks.

scholarly journals Assessing the Performance of Two Bioinspired Algorithms to Solve Single-Row Layout Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Berna Haktanirlar Ulutas
Keyword(s):  
Clonal Selection ◽  
Test Problems ◽  
Clonal Selection Algorithm ◽  
Layout Problem ◽  
Single Row ◽  
One Dimensional ◽  
Straight Line ◽  
Bacterial Foraging Algorithm ◽  
The One ◽  
Bioinspired Algorithms

The single-row layout problem (SRLP), also known as the one-dimensional layout problem, deals with arranging a number of rectangular machines/departments with equal or varying dimensions on a straight line. Since the problem is proved to be NP-hard, there are several heuristics developed to solve the problem. This study introduces both a Clonal Selection Algorithm (CSA) and a Bacterial Foraging Algorithm (BFA) for SRLP. The performance of the algorithms is assessed by using three (small, medium, and large sized) well known test problems available in the literature. The promising results illustrated that both algorithms had generated the best known solutions so far for most of the problems or provided better results for a number of problems.

scholarly journals A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 396
Author(s):  
Roman Cherniha ◽  
Joanna Stachowska-Pietka ◽  
Jacek Waniewski
Keyword(s):  
Solute Transport ◽  
Lie Symmetry ◽  
Transport Processes ◽  
Experimental Investigations ◽  
One Dimensional ◽  
Poroelastic Media ◽  
Poroelastic Materials ◽  
Dimensional Version ◽  
The One ◽  
Symmetry Method

Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail.

scholarly journals On the thermoelasticity with two porosities: asymptotic behaviour

2018 ◽  
Vol 24 (9) ◽  
pp. 2713-2725 ◽  
Author(s):  
N. Bazarra ◽  
J.R. Fernández ◽  
M.C. Leseduarte ◽  
A. Magaña ◽  
R. Quintanilla
Keyword(s):  
Asymptotic Stability ◽  
Exponential Decay ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Porous Structures ◽  
One Dimensional ◽  
Dimensional Version ◽  
The One

In this paper we consider the one-dimensional version of thermoelasticity with two porous structures and porous dissipation on one or both of them. We first give an existence and uniqueness result by means of semigroup theory. Exponential decay of the solutions is obtained when porous dissipation is assumed for each porous structure. Later, we consider dissipation only on one of the porous structures and we prove that, under appropriate conditions on the coefficients, there exists undamped solutions. Therefore, asymptotic stability cannot be expected in general. However, we are able to give suitable sufficient conditions for the constitutive coefficients to guarantee the exponential decay of the solutions.

Dynamic Construction of Voronoi Diagram for a Set of Points and Straight Line Segments

2014 ◽  
Vol 533 ◽  
pp. 264-267
Author(s):  
Xin Liu
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Line Segments ◽  
Potential Value ◽  
Straight Line ◽  
Traditional Algorithm ◽  
Set Of Points

Voronoi Diagram for a set of points and straight line segments is difficult to construct because general figures have uncertain shapes[. In traditional algorithm, when generator of general figure changes, production process will be extremely complex because of the change of regions neighboring with those generator changed. In this paper, we use dynamicconstruction of Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm[2]. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

scholarly journals HEAT TRANSPORT IN A THREE-DIMENSIONAL SLAB GEOMETRY AND THE TEMPERATURE PROFILE OF INGEN-HAUSZ'S EXPERIMENT

2013 ◽  
Vol 27 (13) ◽  
pp. 1350057 ◽  
Author(s):  
SHILADITYA ACHARYA ◽  
KRISHNENDU MUKHERJEE
Keyword(s):  
Temperature Profile ◽  
Three Dimensional ◽  
Initial State ◽  
Slab Geometry ◽  
Similar Nature ◽  
One Dimensional ◽  
Different Temperatures ◽  
Dimensional Version ◽  
The One ◽  
The Continuum

We study the transport of heat in a three-dimensional, harmonic crystal of slab geometry whose boundaries and the intermediate surfaces are connected to stochastic, white noise heat baths at different temperatures. Heat baths at the intermediate surfaces are required to fix the initial state of the slab in respect of its surroundings. We allow the flow of energy fluxes between the intermediate surfaces and the attached baths and impose conditions that relate the widths of Gaussian noises of the intermediate baths. The radiated heat obeys Newton's law of cooling when intermediate baths collectively constitute the environment surrounding the slab. We show that Fourier's law holds in the continuum limit. We obtain an exponentially falling temperature profile from high to low temperature end of the slab and this very nature of the profile was already confirmed by Ingen-Hausz's experiment. Temperature profile of similar nature is also obtained in the one-dimensional version of this model.

On a Square Packing Problem

2002 ◽  
Vol 11 (2) ◽  
pp. 113-127
Author(s):  
S. BOUCHERON ◽  
W. FERNANDEZ de la VEGA
Keyword(s):  
Packing Problem ◽  
Concentration Of Measure ◽  
Change Of Measure ◽  
Tail Probabilities ◽  
One Dimensional ◽  
Large Fluctuations ◽  
Dimensional Version ◽  
Square Packing ◽  
The One ◽  
Average Size

An instance of the square packing problem consists of n squares with independently, uniformly distributed side-lengths and independently, uniformly distributed locations on the unit d-dimensional torus. A packing is a maximum family of pairwise disjoint squares. The one-dimensional version of the problem is the classical random interval packing problem. This paper deals with the asymptotic behaviour of packings as n tends to infinity while d = 2. Coffman, Lueker, Spencer and Winkler recently proved that the average size of packing is Θ(nd/(d+1)). Using partitioning techniques, sub-additivity and concentration of measure arguments, we show first that, after normalization by n2/3, the size of two-dimensional square packings tends in probability toward a genuine limit γ. Straightforward concentration arguments show that large fluctuations of order n2/3 should have probability vanishing exponentially fast with n2/3. Even though γ remains unknown, using a change of measure argument we show that this upper bound on tail probabilities is qualitatively correct.

Parallel Techniques for the Virtual Cell

2005 ◽  
Vol 1 (2) ◽  
pp. 69-74
Author(s):  
Sanguthevar Rajasekaran ◽  
Reda A. Ammar ◽  
Betsy Cheriyan ◽  
Leslie Loew
Keyword(s):  
Parallel Implementation ◽  
Biological Processes ◽  
Cell Analysis ◽  
One Dimensional ◽  
Virtual Cell ◽  
Model Cell ◽  
Dimensional Version ◽  
The One ◽  
Parallel Techniques ◽  
National Resource

The Virtual Cell is a simulation package created by the National Resource for Cell Analysis and Modeling (NRCAM). It enables users to model cell biological processes [1]. The core of the Virtual Cell is solving a system of PDEs. Sequential runs of the Virtual Cell can take large amounts of time and hence parallelization is needed. In this paper we present a parallel implementation of a model that is inspired by the one-dimensional version of the Virtual Cell. Our experimental results show that this parallelization is quite effective. In particular, the speedups we obtain are good implying that the parallel techniques employed could improve the performance of the Virtual Cell.

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