3,108 research outputs found
Local and global properties of conformally flat initial data for black hole collisions
We study physical properties of conformal initial value data for single and
binary black hole configurations obtained using conformal-imaging and
conformal-puncture methods. We investigate how the total mass M_tot of a
dataset with two black holes depends on the configuration of linear or angular
momentum and separation of the holes. The asymptotic behavior of M_tot with
increasing separation allows us to make conclusions about an unphysical
``junk'' gravitation field introduced in the solutions by the conformal
approaches. We also calculate the spatial distribution of scalar invariants of
the Riemann tensor which determine the gravitational tidal forces. For single
black hole configurations, these are compared to known analytical solutions.
Spatial distribution of the invariants allows us to make certain conclusions
about the local distribution of the additional field in the numerical datasets
A Monte Carlo study of temperature-programmed desorption spectra with attractive lateral interactions
We present results of a Monte Carlo study of temperature-programmed
desorption in a model system with attractive lateral interactions. It is shown
that even for weak interactions there are large shifts of the peak maximum
temperatures with initial coverage. The system has a transition temperature
below which the desorption has a negative order. An analytical expression for
this temperature is derived. The relation between the model and real systems is
discussed.Comment: Accepted for publication in Phys.Rev.B15, 10 pages (REVTeX), 2
figures (PostScript); discussion about Xe/Pt(111) adde
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
We study the Parallel Task Scheduling problem with a
constant number of machines. This problem is known to be strongly NP-complete
for each , while it is solvable in pseudo-polynomial time for each . We give a positive answer to the long-standing open question whether
this problem is strongly -complete for . As a second result, we
improve the lower bound of for approximating pseudo-polynomial
Strip Packing to . Since the best known approximation algorithm
for this problem has a ratio of , this result
narrows the gap between approximation ratio and inapproximability result by a
significant step. Both results are proven by a reduction from the strongly
-complete problem 3-Partition
Adaptive mesh refinement approach to construction of initial data for black hole collisions
The initial data for black hole collisions is constructed using a
conformal-imaging approach and a new adaptive mesh refinement technique, a
fully threaded tree (FTT). We developed a second-order accurate approach to the
solution of the constraint equations on a non-uniformly refined high resolution
Cartesian mesh including second-order accurate treatment of boundary conditions
at the black hole throats. Results of test computations show convergence of the
solution as the numerical resolution is increased. FTT-based mesh refinement
reduces the required memory and computer time by several orders of magnitude
compared to a uniform grid. This opens up the possibility of using Cartesian
meshes for very high resolution simulations of black hole collisions.Comment: 13 pages, 11 figure
Bond breaking in vibrationally excited methane on transition metal catalysts
The role of vibrational excitation of a single mode in the scattering of
methane is studied by wave packet simulations of oriented CH4 and CD4 molecules
from a flat surface. All nine internal vibrations are included. In the
translational energy range from 32 up to 128 kJ/mol we find that initial
vibrational excitations enhance the transfer of translational energy towards
vibrational energy and increase the accessibility of the entrance channel for
dissociation. Our simulations predict that initial vibrational excitations of
the asymmetrical stretch (nu_3) and especially the symmetrical stretch (nu_1)
modes will give the highest enhancement of the dissociation probability of
methane.Comment: 4 pages REVTeX, 2 figures (eps), to be published in Phys. Rev. B.
(See also arXiv:physics.chem-ph/0003031). Journal version at
http://publish.aps.org/abstract/PRB/v61/p1565
Spiral Orbit Tribometer
The spiral orbit tribometer (SOT) bridges the gap between full-scale life testing and typically unrealistic accelerated life testing of ball-bearing lubricants in conjunction with bearing ball and race materials. The SOT operates under realistic conditions and quickly produces results, thereby providing information that can guide the selection of lubricant, ball, and race materials early in a design process. The SOT is based upon a simplified, retainerless thrust bearing comprising one ball between flat races (see figure). The SOT measures lubricant consumption and degradation rates and friction coefficients in boundary lubricated rolling and pivoting contacts. The ball is pressed between the lower and upper races with a controlled force and the lower plate is rotated. The combination of load and rotation causes the ball to move in a nearly circular orbit that is, more precisely, an opening spiral. The spiral s pitch is directly related to the friction coefficient. At the end of the orbit, the ball contacts the guide plate, restoring the orbit to its original radius. The orbit is repeatable throughout the entire test. A force transducer, mounted in-line with the guide plate, measures the force between the ball and the guide plate, which directly relates to the friction coefficient. The SOT, shown in the figure, can operate in under ultra-high vacuum (10(exp -9) Torr) or in a variety of gases at atmospheric pressure. The load force can be adjusted between 45 and 450 N. By varying the load force and ball diameter, mean Hertzian stresses between 0.5 and 5.0 GPa can be obtained. The ball s orbital speed range is between 1 and 100 rpm
Experimental Study of Load Carrying Capacity of Point Contacts at Zero Entrainment Velocity
A capacitance technique was used to monitor the film thickness separating two steel balls while subjecting the ball-ball contact to highly stressed, zero entrainment velocity conditions. Tests were performed in a nitrogen atmosphere and utilized 52100 steel balls and a polyalphaolefin lubricant. Capacitance to film thickness accuracy was verified under pure rolling conditions using established EHL theory. Zero entrainment velocity tests were performed at sliding speeds from 6.0 to 10.0 m/s and for sustained amounts of time to 28.8 min. The protective lubricant film separating the specimens at zero entrainment velocity had a film thickness between 0.10 to 0.14 microns (4 to 6 micro in.), which corresponded to a k value of 4. The formation of an immobile surface film formed by lubricant entrapment is discussed as an explanation of the load carrying capacity at zero entrainment velocity conditions, relevant to the ball-ball contacts occurring in retainerless ball bearings
Polynomial Kernels for Weighted Problems
Kernelization is a formalization of efficient preprocessing for NP-hard
problems using the framework of parameterized complexity. Among open problems
in kernelization it has been asked many times whether there are deterministic
polynomial kernelizations for Subset Sum and Knapsack when parameterized by the
number of items.
We answer both questions affirmatively by using an algorithm for compressing
numbers due to Frank and Tardos (Combinatorica 1987). This result had been
first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We
further illustrate its applicability by giving polynomial kernels also for
weighted versions of several well-studied parameterized problems. Furthermore,
when parameterized by the different item sizes we obtain a polynomial
kernelization for Subset Sum and an exponential kernelization for Knapsack.
Finally, we also obtain kernelization results for polynomial integer programs
The Effect of Stress and TiC Coated Balls on Lubricant Lifetimes Using a Vacuum Ball-on-Plate Rolling Contact Tribometer
A vacuum ball-on-plate rolling contact tribometer was used to determine the relative lifetimes of a perfluoropolyether (Krytox 143 AC) on 440C stainless steel. The effect of mean Hertzian stresses (0.75, 1.0, 1.5 and 2.0 GPa) and the use of TiC coated balls on lubricant lifetime was studied. Other conditions included: approximately 100 rpm, approximately 50 micrograms of lubricant, an initial vacuum level of less than 1.0 x 1O(exp -8) Torr, and room temperature (approximately 23 C). increasing the mean Hertzian stress from 0.75 to 2.0 GPa results in an exponential decrease in lubricant lifetime for both material combinations. However. substituting a TiC ball for the 440C ball quadrupled lifetime at low stress levels (0.75 and 1.0 GPa) and doubled life at higher stresses (1.5 and 2.0 GPa). The reduced reactivity of the TiC surface with the PFPE lubricant is considered to be the reason for this enhancement. Decreasing lifetime with increasing stress levels correlated well with energy dissipation calculations
Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2
In this paper we study variants of the non-preemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + ε)OPT can be calculated in polynomial time. Unless P = NP, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case, where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most (1.5 + ε)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios
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