1,735 research outputs found
The Optimal Rubbling Number of Ladders, Prisms and M\"obius-ladders
A pebbling move on a graph removes two pebbles at a vertex and adds one
pebble at an adjacent vertex. Rubbling is a version of pebbling where an
additional move is allowed. In this new move, one pebble each is removed at
vertices and adjacent to a vertex , and an extra pebble is added at
vertex . A vertex is reachable from a pebble distribution if it is possible
to move a pebble to that vertex using rubbling moves. The optimal rubbling
number is the smallest number needed to guarantee a pebble distribution of
pebbles from which any vertex is reachable. We determine the optimal
rubbling number of ladders (), prisms () and
M\"oblus-ladders
Constructions for the optimal pebbling of grids
In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics]
the authors conjecture that if every vertex of an infinite square grid is
reachable from a pebble distribution, then the covering ratio of this
distribution is at most . First we present such a distribution with
covering ratio , disproving the conjecture. The authors in the above paper
also claim to prove that the covering ratio of any pebble distribution is at
most . The proof contains some errors. We present a few interesting
pebble distributions that this proof does not seem to cover and highlight some
other difficulties of this topic
Analytic solutions of the Madelung equation
We present analytic self-similar solutions for the one, two and three
dimensional Madelung hydrodynamical equation for a free particle. There is a
direct connection between the zeros of the Madelung fluid density and the
magnitude of the quantum potential.Comment: 10 pages, 3 figure
Evidence for suppression of collective magnetism in Fe-Ag granular multilayers
Evidence for the suppression of collective magnetic behavior of dipolarly
interacting Fe nanoparticles is found in Fe-Ag granular multilayers.
Interaction of Fe particles located in neighboring Fe layers is studied as a
function of the nominal thickness of the Ag layer in between only two Fe
layers. The surprisingly increasing interaction with increasing Ag-layer
thickness, verified by memory-effect measurements, is explained by the
formation of pinholes in the Ag layer at small Ag thicknesses, allowing direct
ferromagnetic coupling between Fe particles in neighboring Fe layers which may
hinder the frustration of superspins favored by dipolar interactions. At larger
Ag thicknesses, the Ag layer is continuous without pinholes and frustration
leads to the appearance of the superspin-glass state. The effect of increasing
interactions correlates well with the growing deviation at low temperatures of
the measured field-cooled (FC) magnetization from the interaction-free FC curve
calculated by a model based on the relaxation of two-level systems. Similar
phenomenon is reported in a recently published paper (S\'anchez et al., Small
2022, 18, 2106762) where a dense nanoparticle system is studied. The collective
magnetic behavior of the particles due to dipolar interactions is suppressed
when the anisotropy energy of the individual particles exceeds a certain
threshold.Comment: 13 pages, 3 figure
Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities
Two problems will be considered: the question of hidden parameters and the
problem of Kolmogorovity of quantum probabilities. Both of them will be
analyzed from the point of view of two distinct understandings of quantum
mechanical probabilities. Our analysis will be focused, as a particular
example, on the Aspect-type EPR experiment. It will be shown that the quantum
mechanical probabilities appearing in this experiment can be consistently
understood as conditional probabilities without any paradoxical consequences.
Therefore, nothing implies in the Aspect experiment that quantum theory is
incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and
uuencoded postscript, a uuencoded version of a demo program file (epr.exe for
DOS) is attached as a "Figure
Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: I. Transitions in the one-phase liquid region
The published version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsThe phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag-Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of approximately 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model classical nucleation theory (CNT) and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.This work has been supported by the Hungarian Academy of Sciences under Contract No. OTKA-K-62588 and by the ESA PECS Contract Nos. 98005, 98021, and 98043
Phase field theory of crystal nucleation in hard sphere liquid
The phase field theory of crystal nucleation described in [L. Granasy, T.
Borzsonyi, T. Pusztai, Phys. Rev. Lett. 88, 206105 (2002)] is applied for
nucleation in hard--sphere liquids. The exact thermodynamics from molecular
dynamics is used. The interface thickness for phase field is evaluated from the
cross--interfacial variation of the height of the singlet density peaks. The
model parameters are fixed in equilibrium so that the free energy and thickness
of the (111), (110), and (100) interfaces from molecular dynamics are
recovered. The density profiles predicted without adjustable parameters are in
a good agreement with the filtered densities from the simulations. Assuming
spherical symmetry, we evaluate the height of the nucleation barrier and the
Tolman length without adjustable parameters. The barrier heights calculated
with the properties of the (111) and (110) interfaces envelope the Monte Carlo
results, while those obtained with the average interface properties fall very
close to the exact values. In contrast, the classical sharp interface model
considerably underestimates the height of the nucleation barrier. We find that
the Tolman length is positive for small clusters and decreases with increasing
size, a trend consistent with computer simulations.Comment: 7 pages, 7 figure
Artificial Intelligence Usage Opportunities in Smart City Data Management
In our current study, we are aiming to explore data management methods in Smart
City systems. In data management, Artificial Intelligence can be used as well.
Solutions for the usage of Artificial Intelligence and integration into Smart
City concept will be researched as well. Main motivation of the study is to draw
attention to one of the most important element of Smart Cities, to the flow of
data. Our study provides a possible solution for managing data and keep data
up-to-date in such systems with the usage of newest technology possibilities.
While explaining the solution, we will give all the necessary details about the
data flow model between the Artificial Intelligence based system and humans who
are using the Smart City. For managing the dataflow, we would like to use Big
Data methods extended with other required methods. We are using the term of Big
Data as a technology maximizing computation power and algorithmic accuracy to
gather, analyse, link, and compare large data sets [1] connecting with Artificial Intelligence solutions
Analytic solutions of a two-fluid hydrodynamic model
We investigate a one dimensional flow described with the non-compressible
coupled Euler and non-compressible Navier-Stokes equations in Cartesian
coordinate systems. We couple the two fluids through the continuity equation
where different void fractions can be considered. The well-known self-similar
Ansatz was applied and analytic solutions were derived for both velocity and
pressure field as well. The solutions can be expressed with the error
functions.Comment: 11 pages, 4 figure
Upper Bound on the Optimal Rubbling Number in graphs with given minimum degree
A pebbling move on a graph removes two pebbles at a vertex and adds
one pebble at an adjacent vertex. A vertex is reachable
from a pebble distribution if it is possible to move a pebble to
that vertex using pebbling moves. The optimal pebbling number is
the smallest number needed to guarantee a pebble distribution of
pebbles from which any vertex is reachable. Czygrinow proved that
the optimal pebbling number of a graph is at most , where is the number of the vertices and is
the minimum degree of the graph. We improve this result and show that the optimal pebbling number is at most
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