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

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

Difference between male and female rats in vasopressor response to arginine vasopressin

A study was carried out how the sexual difference influences the increase in blood pressure (BP) induced by arginine vasopressin (AVP), and how the binding characteristics of 3H-labelled AVP on membranes prepared from the vascular bed were affected. After the administration of various doses of AVP, a significantly higher BP increase was observed in male rats than in females. The vasopressor effect of AVP was reduced in males following orchidectomy or administration of the antiandrogen cyproterone acetate. The vasopressin (VP) antagonist d(CH2)5Tyr(Me)AVP diminished the BP response to AVP in both sexes. The plasma AVP level was found to be much higher in males than in females, but it was decreased to the level of females after orchidectomy. The density of AVP-binding sites in the aorta membrane preparation was smaller in females, and in orchidectomized or cyproterone acetate-treated male rats than in the control males. The results demonstrate that testosterone upregulates the number of AVP-binding sites, leading to an increase in the pressor response to AVP in the rat vascular bed

Vibrational modes and spectrum of oscillators on a scale-free network

We study vibrational modes and spectrum of a model system of atoms and springs on a scale-free network in order to understand the nature of excitations with many degrees of freedom on the scale-free network. We assume that the atoms and springs are distributed as nodes and links of a scale-free network, assigning the mass $M_{i}$ and the specific oscillation frequency $\omega_{i}$ of the $i$-th atom and the spring constant $K_{ij}$ between the $i$-th and $j$-th atoms.Comment: 8pages, 2 figure

Exactly solvable scale-free network model

We study a deterministic scale-free network recently proposed by Barab\'{a}si, Ravasz and Vicsek. We find that there are two types of nodes: the hub and rim nodes, which form a bipartite structure of the network. We first derive the exact numbers $P(k)$ of nodes with degree $k$ for the hub and rim nodes in each generation of the network, respectively. Using this, we obtain the exact exponents of the distribution function $P(k)$ of nodes with $k$ degree in the asymptotic limit of $k \to \infty$. We show that the degree distribution for the hub nodes exhibits the scale-free nature, $P(k) \propto k^{-\gamma}$ with $\gamma = \ln3/\ln2 = 1.584962$, while the degree distribution for the rim nodes is given by $P(k) \propto e^{-\gamma'k}$ with $\gamma' = \ln(3/2) = 0.405465$. Second, we numerically as well as analytically calculate the spectra of the adjacency matrix $A$ for representing topology of the network. We also analytically obtain the exact number of degeneracy at each eigenvalue in the network. The density of states (i.e., the distribution function of eigenvalues) exhibits the fractal nature with respect to the degeneracy. Third, we study the mathematical structure of the determinant of the eigenequation for the adjacency matrix. Fourth, we study hidden symmetry, zero modes and its index theorem in the deterministic scale-free network. Finally, we study the nature of the maximum eigenvalue in the spectrum of the deterministic scale-free network. We will prove several theorems for it, using some mathematical theorems. Thus, we show that most of all important quantities in the network theory can be analytically obtained in the deterministic scale-free network model of Barab\'{a}si, Ravasz and Vicsek. Therefore, we may call this network model the exactly solvable scale-free network.Comment: 18 pages, 5 figure

Banking applications of FCM models

Fuzzy Cognitive Map (FCMs) is an appropriate tool to describe, qualitatively analyze or simulate the behavior of complex systems. FCMs are bipolar fuzzy graphs: their building blocks are the concepts and the arcs. Concepts represent the most important components of the system, the weighted arcs define the strength and direction of cause-effect relationships among them. FCMs are created by experts in several cases. Despite the best intention the models may contain subjective information even if it was created by multiple experts. An inaccurate model may lead to misleading results, therefore it should be further analyzed before usage. Our method is able to automatically modify the connection weights and to test the effect of these changes. This way the hidden behavior of the model and the most influencing concepts can be mapped. Using the results the experts may modify the original model in order to achieve their goal. In this paper the internal operation of a department of a bank is modeled by FCM. The authors show how the modification of the connection weights affect the operation of the institute. This way it is easier to understand the working of the bank, and the most threatening dangers of the system getting into an unstable (chaotic or cyclic state) can be identified and timely preparations become possible. © Springer Nature Switzerland AG 2019.Peer reviewe

Robust Fixed Point Transformations in Adaptive Control Using Local Basin of Attraction

A further step towards a novel approach to adaptive nonlinear control developed at Budapest Tech in the past few years is reported. This approach obviates the use of the complicated Lyapunov function technique that normally provides global stability of convergence at the costs of both formal and essential restrictions, by applying Cauchy sequences of local, bounded basin of attraction in an iterative control that is free of such restrictions. Its main point is the creation of a robust iterative sequence that only slightly depends on the features of the controlled system and mainly is determined be the control parameters applied. It is shown that as far as its operation is considered the proposed method can be located between the robust Variable Structure / Sliding Mode and the adaptive Slotine-Li control in the case of robots or other Classical Mechanical Systems. The operation of these method is comparatively analyzed for a wheel + connected mass system in which this latter component is “stabilized” along one of the spokes of the wheel in the radial direction by an elastic spring. The robustness of these methods is also investigated againts unknown external disturbances of quite significant amplitudes. The numerical simulations substantiate the superiority of the robust fixed point transformations in the terms of accuracy, simplicity, and smoothness of the control signals applied.N/

Preliminary Sketch of Possible Fixed Point Transformations for Use in Adaptive Control

In this paper a further step towards a novel approach to adaptive nonlinear control developed at Budapest Tech in the past few years is reported. Its main advantage in comparison with the complicated Lyapunov function based techniques is that it is based on simple geometric considerations on the basis of which the control task can be formulated as a Fixed Point Problem for the solution of which a Contractive Mapping is created that generates an Iterative Cauchy Sequence for Single Input - Single Output (SISO) systems. Consequently it converges to the fixed point that is the solution of the control task. In the formerly developed approaches for monotone increasing or monotone decreasing systems the proper fixed points had only a finite basin of attraction outside of which the iteration might become divergent. The here sketched potential solutions apply a special function built up of the “response function” of the excited system under control and of a few parameters. This function has almost constant value apart from a finite region in which it has a “wrinkle” in the vicinity of the desired solution that is the “proper” fixed point of this function. By the use of an affine approximation of the response function around the solution it is shown that at one of its sides this fixed point is repulsive, while at the opposite side it is attractive. It is shown, too, that at the repulsive side another, so called “false” fixed point is present that is globally attractive, with the exception of the basin of attraction of the “proper” one. This structure is advantageous because a) no divergence can occur in the iteration, b) the convergence to the “false” value can easily be detected, and c) by using some ancillary tricks in the most of the cases the solution can be kicked from the wrong fixed point into the basin of attraction of the “proper one”. In the paper preliminary calculations are presented.N/

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof