The technology transfer of non-ferrous alloys casting during the middle age

The article reports on the findings from the metallographic analysis of 13th c. archaeological objects from Chełm (eastern Poland). The group submitted for analysis includes jeweller’s dies used in the production of women’s ceremonial ornaments, crucibles and bronze ornaments. The Mongol invasion of 13th c. had caused craftsmen from central areas of East Europe to flee and seek shelter in the western parts of Rus. It may be safe to interpret the finds from Chełm as the remains of a jeweller’s workshop, the site of casting and working copper alloys and silver. The analysis of the technology used in casting copper alloys and silver in the jeweller’s workshop were made using optical microscopy, X-ray spectroscopy and X-ray radiography

Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to $\exp(-\alpha x)$ of selection of neighbours against distance $x$. The network nodes are endowed with spin-like variables $s_i = \pm 1$, with Ising interaction $J>0$. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature $T_c$ is close to 3.8 for $\alpha < 0.0$ and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action {\it via} weak ties, as discussed by Granovetter in 1973.Comment: 10 pages, 7 figure

Self-consistent Wigner distribution function study of gate-voltage controlled triple-barrier resonant tunnelling diode

The electron transport through the triple-barrier resonant tunnelling diode (TBRTD) have been studied by the self-consistent numerical method for the Wigner-Poisson problem. The electron flow through the TBRTD can be controlled by the gate voltage applied to one of the potential well regions. For different gate voltage values we have determined the current-voltage characteristics, potential energy profiles, and electron density distribution. We have found the enhancement of the peak-to-valley ratio (up to $\sim$10), the appearance of the linear current versus bias voltage behaviour within the negative-differential resistance region, and the bistability of the current-voltage characteristics. The analysis of the self-consistent potential energy profiles and electron density distribution allowed us to provide a physical interpretation of these properties.Comment: 13 pages, 7 figure

Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions.Comment: 10 pages, 9 figure

Application program SMATH in analysis of staeady state of electrical circuits

W pracy zaprezentowano oprogramowanie pomocne w nauczaniu studentów analizy obwodów elektrycznych [1]. Programy utworzone w systemie SMATH [2] umożliwiające rozwiązać zadania z obwodów elektrycznych, stanowią interesujące narzędzie wspomagające proces nauczania. Możliwość tworzenia przez studentów własnych struktur obwodów elektrycznych, z podglądem zastosowanych w obliczeniach równań i wyników tych obliczeń jest ciekawą alternatywą nauki dla studentów.The paper presents the software useful in teaching students the analysis of electrical circuits [1]. Programs created in the system SMath [2] allow to solve the tasks of electrical circuits, provide interesting tool to support the learning process. The ability to create their own structures by students of electrical circuits, the preview used in the calculation equations and the results of these calculations is an interesting alternative learning for students

Using SMATH software for the analysis of steady states in electric circuits

This paper presents software that can be used for educational purposes – teaching students to perform the analysis of electric circuits [1]. Programmes created in the SMATH system [2] make it possible to solve exercises on electric circuits and constitute an interesting tool supporting the teaching process. The fact that the students can form their own electric circuit structures, with a preview of the equations and the solutions of these calculations, offers to them an interesting learning alternative

Magnetic field vector gradiometer

W pracy przedstawiono metodę wyznaczania parametrów wektorowego gradiometru magnetycznego mających istotny wpływ na przybliżony pomiar pochodnych cząstkowych. Wartości pochodnych cząstkowych mierzone są w sposób przybliżony metodą różnicową. Dokładność pomiaru różnicy indukcji magnetycznej zależy od kąta przesunięcia osi czujników magnetycznych, przesunięcia zera i współczynnika skali czujników oraz od odległości między czujnikami. Skuteczność wykrywania obiektów ferromagnetycznych z zastosowaniem wektorowego gradiometru bez informacji o wartościach tych parametrów jest bardzo niska.Five independent partial derivatives of the magnetic flux density vector are used for detecting ferromagnetic objects by use of vector gradiometers in algorithms of object locating and identifying. This method requires precise measurement of the magnetic flux density gradient (1). A gradiometer built of magnetometers with directional sensitivity characteristics has several parameters, called critical in this paper, that influence the measurement of partial derivatives in a significant way. The gradiometer critical parameters are: angle between the axis of magnetic sensors, offset, accuracy of measurements of separate sensors and the distance between them. The critical parameters values can be determined on a basis of measurements from formulas (4-8). Partial derivatives (1) are determined on a basis of measuring the difference quotient of the magnetic flux density. When choosing the distance sensors, their sensitivity and approximation of partial derivatives by difference quotients should be taken into account