Study of a model for the distribution of wealth

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.Comment: 12 pages, 2 figure

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.Comment: 4 pages, 2 figures; you can also visit http://add.unizar.es/public/100_16613/index.htm

Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers

We consider three examples of weekly perturbed centers which do not have {\it geometrical equivalence}: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: $dH(x,y)+\epsilon(f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)={1/2}(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)=\int_{H=h}fdy-gdx$, associated to each particular problem. We obtain the information on the bifurcation curves of the limit cycles by solving explicitly the equation $M(h)=0$ in each case.Comment: 17 pages, 0 figure

A method to discern complexity in two-dimensional patterns generated by coupled map lattices

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where the system displays spatio-temporal intermittency.Comment: 3 pages, 3 figures; some information about the authors: http://add.unizar.es/public/100_16613/index.htm

Data reduction in the ITMS system through a data acquisition model with self-adaptive sampling rate

Long pulse or steady state operation of fusion experiments require data acquisition and processing systems that reduce the volume of data involved. The availability of self-adaptive sampling rate systems and the use of real-time lossless data compression techniques can help solve these problems. The former is important for continuous adaptation of sampling frequency for experimental requirements. The latter allows the maintenance of continuous digitization under limited memory conditions. This can be achieved by permanent transmission of compressed data to other systems. The compacted transfer ensures the use of minimum bandwidth. This paper presents an implementation based on intelligent test and measurement system (ITMS), a data acquisition system architecture with multiprocessing capabilities that permits it to adapt the system’s sampling frequency throughout the experiment. The sampling rate can be controlled depending on the experiment’s specific requirements by using an external dc voltage signal or by defining user events through software. The system takes advantage of the high processing capabilities of the ITMS platform to implement a data reduction mechanism based in lossless data compression algorithms which are themselves based in periodic deltas

Nonlinear Interaction of Transversal Modes in a CO2 Laser

We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.Comment: 16 pages, 0 figure

Modelización geoquímica de los procesos de fusión parcial

18 páginas, 6 figuras, 1 apendice.[ES] Durante la fusión, los elementos traza y los isótopos estables sufren fraccionación mientras que los isótopos radiogénicos no varían. Como la distribución de los primeros entre las fases que intervienen sigue las leyes de las soluciones diluidas, se pueden establecer ecuaciones relativamente sencillas, que posibilitan la modelización del proceso. A su vez, el comportamiento de los isótopos radiogénicos hace que los magmas hereden la signatura del sólido del que derivar, lo que facilita la identificación del mismo. Las ecuaciones propuestas para los diferentes tipos de fusión indican que en la fusión en equilibrio la abundancia en el fundido de elementos traza altamente incompatibles alcanza valores muy elevados al comienzo del proceso y disminuye progresivamente al aumentar el grado de fusión, mientras que la concentración de los elementos compatibles crece lentamente al aumentar el porcentaje de fusión y bruscamente cuando éste alcanza valores muy altos. En la fusión fraccionada el primero de los líquidos que se genera removiliza casi completamente a todos los elementos altamente incompatibles del sistema, y los sucesivos líquidos producidos tienen muy baja concentración en dichos elementos. En la fusión incongruente se generan líquidos ricos en aquellos elementos traza que tienen altos coeficientes de reparto para las fases que funden y bajos para las de nueva formación, mientras que están empobrecidos en los elementos que entran en estas últimas fases. Si la fusión tiene lugar en presencia de una fase fluida el líquido está empobrecido, en relación al generado cuando dicha fase está ausente, en aquellos elementos que tienen coeficientes de reparto líquido-fluido aproximadamente iguales a la unidad, ya que una parte de los mismos se concentra en el fluido. Finalmente, en la fusión en desequilibrio o no difusión a la primera fracción de líquido que aparece tiene una concentración en elementos incompatibles superior y en elementos compatibles inferior a la del sólido del que deriva, con lo que la interfase sólido-líquido se empobrece y se enriquece, respectivamente. Sin embargo, al final del proceso la concentración de los elementos en el líquido se iguala a la que tenía la parte de sólido que ha fundido. Para modelizar la fusión parcid en equilibrio se pueden seguir dos vías diferentes, según se disponga o no de los coefcientes de reparto mineral-líquido y se conozcan o no los porcentajes en los que intervienen dichas fases. Si se dispone de dichos parámetros, se puede intentar duplicar las concentraciones elementales observadas en los líquidos primarios, previa selección de unas constantes razonables. Por el contrario, si no se conocen aquellos parámetros la mJdelización se puede llevar a cabo de forma distinta, según se disponga de la composición de los líquidos generados o del residuo. Si se conoce la composición de los líquidos generados, se utilizan las variaciones en las concentraciones elementales que presentan las rocas, mediante un ajuste simultáneo de todas ellas por resolución de un sistema de ecuaciones formado por las expresiones que describen el proceso, para un número suficiente de elementos, o bien independientemente para cada parámetro y elemento. A su vez, si se conoce la composición química de los residuos hay que suponer la composición del protolito y a partir del elemento más residual fijar los dos parámetros que quedan por conocer: el coeficiente de partición global residuofundido para los distintos elementos y el grado de fusión que ha sufrido cada restita, asumiendo, según proceda, el grado de fusión, el coeficiente de reparto global de uno de los elementos o la concentración del mismo.[EN] During melting processes both stable isotopes and trace elements fractionate, whereas radiogenic isotopes do not change. The distribution of the former between the phases that participate, follows diluted solutions laws in such a way that it is possible to establish relatively simple equations to model these processes. Additionally, the radiogenic isotopes behaviour implies that the magmas retain the source signature thus allowing its identification. In the case of equilibrium melting, the highly incompatible elements abundance is very high in the liquid at the beginning of the process and decreases progressively as the melting degree increases. On the contrary, the concentration in compatible elements grows very slowly during the first steps to increase sharply for the highest F values. During fractional melting, the first liquid generated removes almost all the incompatible elements thus producing a relative depletion in those elements in the successive liquids. In the case of incongruent melting, the magmas are enriched in the trace elements with high distribution coefficients for the phases that melt and low for the newly generated phases, and are impoverished in the elements that constitute the new phases. If melting is produced in the presence of a fluid phase, the liquid will be depleted in those elements with fluid/liquid distribution coefficients close to 1, rdative to the same liquid generated without a fluid phase. Finally, during disequilibrium or nondiffusive melting, the first liquid fraction has a concentration in incompatible dements higher and in compatible elements lower than that in the source, so the solid-liquid interface is depleted and enriched, respectively. However, at the end of the process the concentration of elements in the liquid is equated to the abundance in the solid that melted. To model equilibrium me1ting two diferent approaches can be followed, depending on the availability of the mineral-liquid distribution coefficients and the percentages in which the mineral phases have participated. When these parameters are known, it is possible to duplicate the concentrations observed in the primary liquids by selecting reasonable constants. On the contrary, when these parameters are unknown the approach to follow will depend on the knowledge of the cbmposition of the liquids or that of the residue. In the first case, the element concentrations of tbe rocks are used to obtain a simultaneous best-fit solution of a system constituted by tile equations that describe the process, either for a number of elements, or individually for each parameter and element. If the composition of the residue is known, it is necessary to guess the composition of the protolith. Then, from the most residual element the two remaining parameters (the residue- melt bulk distribution coefficient and the degree of melting of each restite) are defined, either assuming the degree of melting, the elements bulk distribution coefficient, or their concentration.Este trabajo se ha realizado dentro del Proyecto de Investigación PB92-lOS «Magmatismo intraplaca relacionado con puntos calientes en la Península Ibérica», financiado por la Dirección General de Investigación Científica y Técnica.Peer reviewe

Drivers of Business-to-Business (B2B) Sales Success and the role of Digitalization after COVID-19 Disruptions

Purpose - The purpose of this research is to investigate the drivers of business-to-business sales success and the role of digitalization, in a selling and sales management landscape being disrupted by COVID-19. Design/methodology/approach – The methodology follows a discovery-oriented grounded theory approach which consists of a two-stage qualitative study with sales professionals in Chile, and a Fuzzy-Set Qualitative Comparative Analysis (fsQCA). Findings - This research shows that interfunctional coordination, agility in the selling process, and business customer engagement are critical determinants of B2B sales success, while digitalization moderates these relationships. Originality/value - This research responds to a call for more research on the impact of digitalization on business relationships in different contexts and perspectives. We study the Chilean context, through a two-stage qualitative study, and a fsQCA analysis, which constitutes a novel combination in this stream of research

Features of the Extension of a Statistical Measure of Complexity to Continuous Systems

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some choice. In the present study, several possibilities appear available. One of them is examined in detail. Some interesting properties desirable for any magnitude of complexity are discovered on this particular extension.Comment: 22 pages, 0 figure