2,234 research outputs found
Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?
An n-town, for a natural number n, is a group of n buildings, each occupying
a distinct position on a 2-dimensional integer grid. If we measure the distance
between two buildings along the axis-parallel street grid, then an n-town has
optimal shape if the sum of all pairwise Manhattan distances is minimized. This
problem has been studied for cities, i.e., the limiting case of very large n.
For cities, it is known that the optimal shape can be described by a
differential equation, for which no closed-form is known. We show that optimal
n-towns can be computed in O(n^7.5) time. This is also practically useful, as
it allows us to compute optimal solutions up to n=80.Comment: 26 pages, 6 figures, to appear in Computational Geometry: Theory and
Application
The effect of different opacity data and chemical element mixture on the Petersen diagram
The Petersen diagram is a frequently used tool to constrain model parameters
such as metallicity of radial double-mode pulsators. In this diagram the period
ratio of the radial first overtone to the fundamental mode, P_1/P_0, is plotted
against the period of the fundamental mode. The period ratio is sensitive to
the chemical composition as well as to the rotational velocity of a star. In
the present study we compute stellar pulsation models to demonstrate the
sensitivity of the radial period ratio to the opacity data (OPAL and OP tables)
and we also examine the effect of different relative abundances of heavy
elements. We conclude that the comparison with observed period ratios could be
used successfully to test the opacity data.Comment: 5 pages, 5 figures, 1 table; to be published in the Proceedings of
the Conference 'Unsolved Problems in Stellar Physics', Cambridge, 2-6 July
200
Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection
We present experimental results for Rayleigh-Benard convection patterns in a
cylindrical container with static side-wall forcing induced by a heater. This
forcing stabilized a pattern of concentric rolls (a target pattern) with the
central roll (the umbilicus) at the center of the cell after a jump from the
conduction to the convection state. A quasi-static increase of the control
parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off
center. As observed by others, a further quasi-static increase of epsilon up to
15.6 caused a sequence of transitions. Each transition began with the
displacement of the umbilicus and then proceeded with the loss of one
convection roll at the umbilicus and the return of the umbilicus to a location
near the center of the cell. Alternatively, with decreasing epsilon new rolls
formed at the umbilicus but large umbilicus displacements did not occur. In
addition to quantitative measurements of the umbilicus displacement, we
determined and analyzed the entire wave-director field of each image. The wave
numbers varied in the axial direction, with minima at the umbilicus and at the
cell wall and a maximum at a radial position close to 2/3 Gamma. The wave
numbers at the maximum showed hysteretic jumps at the transitions, but on
average agreed well with the theoretical predictions for the wave numbers
selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include
Optimized cryo-EM data-acquisition workflow by sample-thickness determination
Sample thickness is a known key parameter in cryo-electron microscopy (cryo-EM) and can affect the amount of high-resolution information retained in the image. Yet, common data-acquisition approaches in single-particle cryo-EM do not take it into account. Here, it is demonstrated how the sample thickness can be determined before data acquisition, allowing the identification of optimal regions and the restriction of automated data collection to images with preserved high-resolution details. This quality-over-quantity approach almost entirely eliminates the time- and storage-consuming collection of suboptimal images, which are discarded after a recorded session or during early image processing due to a lack of high-resolution information. It maximizes the data-collection efficiency and lowers the electron-microscopy time required per data set. This strategy is especially useful if the speed of data collection is restricted by the microscope hardware and software, or if microscope access time, data transfer, data storage and computational power are a bottleneck
A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS
In this paper we discuss some issues related to Poincar´e’s inequality for aspecial class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties
Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection
For rapidly rotating turbulent Rayleigh–Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra1/4Ek2/3 where the Ekman number Ek decreases with increasing rotation rate
Memory-related cognitive load effects in an interrupted learning task:A model-based explanation
Background: The Cognitive Load Theory provides a well-established framework for investigating aspects of learning situations that demand learners' working memory resources. However, the interplay of these aspects at the cognitive and neural level is still not fully understood. Method: We developed four computational models in the cognitive architecture ACT-R to clarify underlying memory-related strategies and mechanisms. Our models account for human data of an experiment that required participants to perform a symbol sequence learning task with embedded interruptions. We explored the inclusion of subsymbolic mechanisms to explain these data and used our final model to generate fMRI predictions. Results: The final model indicates a reasonable fit for reaction times and accuracy and links the fMRI predictions to the Cognitive Load Theory. Conclusions: Our work emphasizes the influence of task characteristics and supports a process-related view on cognitive load in instructional scenarios. It further contributes to the discussion of underlying mechanisms at a neural level
The Domain Chaos Puzzle and the Calculation of the Structure Factor and Its Half-Width
The disagreement of the scaling of the correlation length xi between
experiment and the Ginzburg-Landau (GL) model for domain chaos was resolved.
The Swift-Hohenberg (SH) domain-chaos model was integrated numerically to
acquire test images to study the effect of a finite image-size on the
extraction of xi from the structure factor (SF). The finite image size had a
significant effect on the SF determined with the Fourier-transform (FT) method.
The maximum entropy method (MEM) was able to overcome this finite image-size
problem and produced fairly accurate SFs for the relatively small image sizes
provided by experiments.
Correlation lengths often have been determined from the second moment of the
SF of chaotic patterns because the functional form of the SF is not known.
Integration of several test functions provided analytic results indicating that
this may not be a reliable method of extracting xi. For both a Gaussian and a
squared SH form, the correlation length xibar=1/sigma, determined from the
variance sigma^2 of the SF, has the same dependence on the control parameter
epsilon as the length xi contained explicitly in the functional forms. However,
for the SH and the Lorentzian forms we find xibar ~ xi^1/2.
Results for xi determined from new experimental data by fitting the
functional forms directly to the experimental SF yielded xi ~ epsilon^-nu} with
nu ~= 1/4 for all four functions in the case of the FT method, but nu ~= 1/2,
in agreement with the GL prediction, in the the case of the MEM. Over a wide
range of epsilon and wave number k, the experimental SFs collapsed onto a
unique curve when appropriately scaled by xi.Comment: 15 pages, 26 figures, 1 tabl
Plume motion and large-scale circulation in a cylindrical Rayleigh-B\'enard cell
We used the time correlation of shadowgraph images to determine the angle
of the horizontal component of the plume velocity above (below) the
center of the bottom (top) plate of a cylindrical Rayleigh-B\'enard cell of
aspect ratio ( is the diameter and mm
the height) in the Rayleigh-number range for a Prandtl number . We expect that gives the
direction of the large-scale circulation. It oscillates time-periodically. Near
the top and bottom plates has the same frequency but is
anti-correlated.Comment: 4 pages, 6 figure
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