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 $v$ and $w$ adjacent to a vertex $u$, and an extra pebble is added at vertex $u$. 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 $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. We determine the optimal rubbling number of ladders ($P_n\square P_2$), prisms ($C_n\square P_2$) 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 $3.25$. First we present such a distribution with covering ratio $3.5$, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most $6.75$. 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 $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. Czygrinow proved that the optimal pebbling number of a graph is at most $\frac{4n}{\delta+1}$, where $n$ is the number of the vertices and $\delta$ is the minimum degree of the graph. We improve this result and show that the optimal pebbling number is at most $\frac{3.75n}{\delta+1}$